74
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Number
$74$ (seventy-four) is:
- $2 \times 37$
- The $1$st element of the $1$st pair of consecutive even nontotients.
- The $2$nd of the $2$nd ordered quadruple of consecutive integers that have divisor sums which are strictly increasing:
- $\map {\sigma_1} {73} = 74$, $\map {\sigma_1} {74} = 114$, $\map {\sigma_1} {75} = 124$, $\map {\sigma_1} {76} = 140$
- The $6$th integer $n$ after $-1$, $0$, $2$, $7$, $15$ such that $\dbinom n 0 + \dbinom n 1 + \dbinom n 2 + \dbinom n 3 = m^2$ for integer $m$:
- $\dbinom {74} 0 + \dbinom {74} 1 + \dbinom {74} 2 + \dbinom {74} 3 = 260^2$
- The $8$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$:
- $\nexists m \in \Z_{>0}: \map \phi m = 74$
- where $\map \phi m$ denotes the Euler $\phi$ function
- The $25$th semiprime:
- $74 = 2 \times 37$
- The $28$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
- $3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $66$, $68$, $69$, $74$, $\ldots$
Also see
- Previous ... Next: Sum of 4 Consecutive Binomial Coefficients forming Square
- Previous ... Next: Nontotient
- Previous ... Next: 91 is Pseudoprime to 35 Bases less than 91
- Previous ... Next: Semiprime Number
- Previous ... Next: Sequences of 4 Consecutive Integers with Rising Divisor Sum
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $74$