A324526 Numbers m such that gcd(sigma(m), pod(m)) = tau(m) where tau(k) = the number of divisors of k (A000005), sigma(k) = the sum of the divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).

1, 14, 22, 38, 46, 56, 62, 86, 94, 110, 118, 134, 142, 150, 158, 166, 184, 206, 214, 254, 262, 278, 286, 302, 326, 334, 342, 358, 374, 382, 398, 422, 430, 446, 454, 478, 486, 494, 502, 504, 526, 542, 566, 568, 612, 614, 622, 638, 646, 662, 670, 694, 718, 726

Offset

1,2

Comments

Numbers n such that A306682(n) = A000005(n).

Links

Table of n, a(n) for n=1..54.

Example

14 is a term because gcd(sigma(14), pod(14)) = gcd(24, 196) = 4 = tau(14).

Prog

(Magma) [n: n in [1..10^5] | GCD(SumOfDivisors(n), &*[d: d in Divisors(n)]) eq NumberOfDivisors(n)]
(PARI) isok(n) = my(d=divisors(n)); gcd(vecsum(d), vecprod(d)) == #d; \\ Michel Marcus, Mar 05 2019

Crossrefs

Cf. A000005, A000203, A007955, A306682.

Sequence in context: A305084 A225710 A183185 * A259750 A211416 A045282

Adjacent sequences: A324523 A324524 A324525 * A324527 A324528 A324529

Keyword

nonn

Author

Jaroslav Krizek, Mar 05 2019

Status

approved