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

1,2

Links

Table of n, a(n) for n=1..42.

Example

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.

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 *)

Prog

(Magma) A309253:=func<n|exists(r){m:m in[1..200000] | #[d: d in Divisors(m) | IsIntegral(m / SumOfDivisors(d))] eq n }select r else 0>; [A309253(n): n in[1..40]]
(PARI) a(n) = my(m=1); while(sumdiv(m, d, !(m%sigma(d))) != n, m++); m; \\ Jinyuan Wang, Aug 08 2019

Crossrefs

Cf. A173441, A326696, A326697, A326698.

Sequence in context: A326858 A165734 A367665 * A260017 A351773 A123624

Adjacent sequences: A309250 A309251 A309252 * A309254 A309255 A309256

Keyword

nonn

Author

Jaroslav Krizek, Aug 08 2019

Status

approved