96

Number

$96$ (ninety-six) is:

$2^5 \times 3$

The $2$nd positive integer after $64$ with $6$ or more prime factors:

$96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3$

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

The $5$th untouchable number after $2$, $5$, $52$, $88$

The $6$th octagonal number, after $1$, $8$, $21$, $40$, $65$:

$96 = 1 + 7 + 13 + 19 + 25 + 31 = 6 \paren {3 \times 6 - 2}$

The $21$st highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$, $16$, $18$, $20$, $24$, $30$, $36$, $42$, $48$, $60$, $72$, $84$, $90$:

$\map {\sigma_1} {96} = 252$

The $22$nd semiperfect number after $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$, $40$, $42$, $48$, $54$, $56$, $60$, $66$, $72$, $78$, $80$, $84$, $88$, $90$:

$96 = 16 + 32 + 48$

The $28$th positive integer which is not the sum of $1$ or more distinct squares:

$2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $33$, $43$, $44$, $47$, $48$, $60$, $67$, $72$, $76$, $92$, $96$, $\ldots$

The $48$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $61$, $65$, $66$, $67$, $72$, $77$, $80$, $81$, $84$, $89$, $94$, $95$ which cannot be expressed as the sum of distinct pentagonal numbers

The $51$st (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $77$, $78$, $79$, $84$, $90$, $91$, $95$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$

There are $17$ positive integers which have an Euler $\phi$ value $96$.