A384665 Smallest odd multiplier k such that k*n is abundant.

945, 9, 315, 3, 189, 3, 135, 3, 105, 3, 315, 1, 315, 3, 63, 3, 315, 1, 315, 1, 45, 3, 315, 1, 63, 3, 35, 3, 315, 1, 315, 3, 105, 3, 27, 1, 315, 3, 105, 1, 315, 1, 315, 3, 21, 3, 315, 1, 45, 3, 105, 3, 315, 1, 63, 1, 105, 3, 315, 1, 315, 3, 15, 3, 63, 1, 315, 3

Offset: 1

Author

Sergio Pimentel, Jun 06 2025

Keywords

• nonn

Comments

a(n) <= 945 for all n. a(n) = 945 for prime numbers > 103.

The possible values appear to be: 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 105, 135, 189, 315, 945. - Michel Marcus, Jun 12 2025

Examples

			a(5) = 189 because 189 is the smallest odd multiplier k such that 5*k is abundant (i.e., 5*189 = 945 which is abundant).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005101, A005231, A023196, A254571.

Programs

Maple

f:= proc(n) local k;
  for k from 1 by 2 do if numtheory:-sigma(n*k) > 2*n*k then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Jun 09 2025

Mathematica

a[n_] := Module[{k = 1}, While[DivisorSigma[-1, k*n] <= 2, k += 2]; k]; Array[a, 100] (* Amiram Eldar, Jun 06 2025 *)

PARI

a(n) = my(k=1); while (sigma(k*n,-1)<=2, k+=2); k; \\ Michel Marcus, Jun 09 2025