87

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Number

$87$ (eighty-seven) is:

$3 \times 29$

The $2$nd positive integer after $1$ whose divisor sum of its Euler $\phi$ value equals its divisor sum:

$\map {\sigma_1} {\map \phi {87} } = \map {\sigma_1} {56} = 120 = \map {\sigma_1} {87}$

The $4$th after $4$, $13$, $38$ in the sequence formed by adding the squares of the first $n$ primes:

$87 = \ds \sum_{i \mathop = 1}^4 {p_i}^2 = 2^2 + 3^2 + 5^2 + 7^2$

The $4$th positive integer after $1$, $24$, $26$ whose Euler $\phi$ value is equal to the product of its digits:

$\map \phi {87} = 56 = 8 \times 7$

The $20$th lucky number:

$1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $79$, $87$, $\ldots$

The $29$th semiprime:

$87 = 3 \times 29$

The $33$rd of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:

$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $66$, $68$, $69$, $74$, $75$, $79$, $81$, $82$, $87$, $\ldots$

Arithmetic Functions on $87$

\(\ds \map \phi { 87 }\)

\(=\)

\(\ds 56\)

$\phi$ of $87$

\(\ds \map {\sigma_1} { 87 }\)

\(=\)

\(\ds 120\)

$\sigma_1$ of $87$

Also see

• Previous  ... Next: Integers for which Divisor Sum of Phi equals Divisor Sum
• Previous  ... Next: Numbers for which Euler Phi Function equals Product of Digits
• Previous  ... Next: Sum of Sequence of Squares of Primes
• Previous  ... Next: Lucky Number
• Previous  ... Next: 91 is Pseudoprime to 35 Bases less than 91
• Previous  ... Next: Semiprime Number

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $87$