98

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Number

$98$ (ninety-eight) is:

$2 \times 7^2$

With $89$, gives the longest reverse-and-add sequence of any $2$-digit integers, of $24$ terms

The $1$st even integer that cannot be expressed as the sum of $2$ prime numbers of which the smaller one is $3$, $5$ or $7$

The $1$st of the $3$rd pair of consecutive integers which both have $6$ divisors:

$\map {\sigma_0} {98} = \map {\sigma_0} {99} = 6$

The $5$th even integer after $2$, $4$, $94$, $96$ that cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes

The $5$th after $0$, $2$, $3$, $27$ of the $6$ integers which are the middle term of a sequence of $5$ consecutive integers whose cubes add up to a square

$96^3 + 97^3 + 98^3 + 99^3 + 100^3 = 4 \, 708 \, 900 = 2170^2$

The $13$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$, $74$, $76$, $86$, $90$, $94$:

$\nexists m \in \Z_{>0}: \map \phi m = 98$

where $\map \phi m$ denotes the Euler $\phi$ function

The $19$th positive integer $n$ after $5$, $11$, $17$, $23$, $29$, $30$, $36$, $42$, $48$, $54$, $60$, $61$, $67$, $73$, $79$, $85$, $91$, $92$ such that no factorial of an integer can end with $n$ zeroes

Also see

• 2-Digit Numbers forming Longest Reverse-and-Add Sequence
• Reciprocal of 98

• Previous  ... Next: Sum of Cubes of 5 Consecutive Integers which is Square
• Previous  ... Next: Pairs of Consecutive Integers with 6 Divisors
• Previous  ... Next: Numbers of Zeroes that Factorial does not end with
• Previous  ... Next: Nontotient
• Previous  ... Next: Even Integers not Sum of 2 Twin Primes

• Next: Even Integers not Expressible as Sum of 3, 5 or 7 with Prime

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $98$