A309253 a(n) is the smallest number m with exactly n such divisors d that sigma(d) divides m.

1, 6, 30, 12, 60, 84, 1140, 120, 168, 2340, 1848, 360, 2184, 1080, 4368, 840, 10440, 1680, 7920, 2520, 6552, 3360, 7560, 5040, 13104, 27720, 73440, 36960, 21840, 15120, 72072, 10080, 95760, 26208, 63840, 20160, 146160, 144144, 87360, 174720, 1071360, 166320

Offset: 1

Author

Jaroslav Krizek, Aug 08 2019

Keywords

• nonn

Examples

			For n = 3; a(3) = 30 because 30 is the smallest number with exactly 3 divisors d that sigma(d) is also its divisor, namely 1, 2 and 5 as sigma(1) = 1, sigma(2) = 3 and sigma(5) = 6, and all these (1, 3 and 6) are divisors of 30.
		

Crossrefs

Cf. A173441, A326696, A326697, A326698.

Programs

Magma

A309253:=func; [A309253(n): n in[1..40]];

Mathematica

f[n_] := Count[Divisors[n], ?(Divisible[n, DivisorSigma[1, #]] &)]; m = 42; s = Table[0, {m}]; c = 0; n = 1; While[c < m, v = f[n]; If[v <=m && s[[v]] == 0, c++; s[[v]] = n]; n++]; s (* _Amiram Eldar, Aug 08 2019 *)

PARI

a(n) = my(m=1); while(sumdiv(m, d, !(m%sigma(d))) != n, m++); m; \\ Jinyuan Wang, Aug 08 2019