77

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Number

$77$ (seventy-seven) is:

$7 \times 11$

The smallest positive integer having a multiplicative persistence of $4$

The $6$th palindromic integer after $0$, $1$, $2$, $3$, $11$ which is the index of a palindromic triangular number

$T_{77} = 3003$

The $7$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$:

$77 = \dfrac {7 \left({3 \times 7 + 1}\right)} 2$

The $10$th integer $m$ such that $m! + 1$ (its factorial plus $1$) is prime:

$0$, $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$

The number of integer partitions for $12$:

$\map p {12} = 77$

The $14$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$:

$77 = \dfrac {7 \left({3 \times 7 + 1}\right)} 2$

The $26$th semiprime:

$77 = 7 \times 11$

The $32$nd odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime

$1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $\ldots$

The $34$th integer $n$ such that $2^n$ contains no zero in its decimal representation:

$2^{77} = 151 \, 115 \, 727 \, 451 \, 828 \, 646 \, 838 \, 272$

The $41$st positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $50$, $54$, $55$, $59$, $60$, $61$, $65$, $66$, $67$, $72$ which cannot be expressed as the sum of distinct pentagonal numbers

The $44$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $55$, $60$, $61$, $65$, $66$, $67$, $72$, $73$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$

The smallest (positive) integer which requires $5$ syllables to say it in the English language:

sev-en-ty-sev-en

The largest positive integer which cannot be expressed as the sum of positive integers whose reciprocals add up to $1$

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Also see

• Positive Integers Expressible by Sum of Integers whose Reciprocals Sum to 1

• Previous  ... Next: Palindromic Indices of Palindromic Triangular Numbers
• Previous  ... Next: Smallest Arguments for given Multiplicative Persistence
• Previous  ... Next: Integer Partition
• Previous  ... Next: Second Pentagonal Number
• Previous  ... Next: Generalized Pentagonal Number
• Previous  ... Next: Odd Numbers Not Expressible as Sum of 4 Distinct Non-Zero Coprime Squares
• Previous  ... Next: Sequence of Integers whose Factorial plus 1 is Prime
• Previous  ... Next: Numbers not Expressible as Sum of Distinct Pentagonal Numbers
• Previous  ... Next: Integers not Expressible as Sum of Distinct Primes of form 6n-1
• Previous  ... Next: Semiprime Number
• Previous  ... Next: Powers of 2 with no Zero in Decimal Representation

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $77$