A324527 a(n) = the smallest number m such that gcd(sigma(m), pod(m)) = n where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).

1, 10, 15, 12, 95, 180, 91, 56, 51, 40, 473, 6, 117, 980, 135, 70, 1139, 90, 703, 290, 861, 26378, 3151, 54, 745, 468, 255, 2156, 5017, 26100, 775, 124, 1419, 2176, 4865, 96, 2701, 26714, 585, 190, 6683, 65268, 11051, 5632, 435, 144946, 13207, 42, 679, 5800

Offset: 1

Author

Jaroslav Krizek, Mar 05 2019

Keywords

• nonn

Comments

a(n) = the smallest number m such that A306682(m) = n.

Examples

			For n=2; a(2) = 10 because gcd(sigma(10), pod(10)) = gcd (18, 100) = 2 and 10 is the smallest.
		

Crossrefs

Cf. A000005, A000203, A007955, A074391, A306682.

Programs

Magma

[Min([n: n in[1..10^5] | GCD(SumOfDivisors(n), &*[d: d in Divisors(n)]) eq k]): k in [1..45]]

PARI

f(n) = my(d=divisors(n)); gcd(vecsum(d), vecprod(d)); \\ A306682
a(n) = {my(k=1); while (f(k) != n, k++); k;} \\ Michel Marcus, Mar 05 2019