cp's OEIS Frontend

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

%I A384665 #25 Jul 06 2025 14:57:25
%S A384665 945,9,315,3,189,3,135,3,105,3,315,1,315,3,63,3,315,1,315,1,45,3,315,
%T A384665 1,63,3,35,3,315,1,315,3,105,3,27,1,315,3,105,1,315,1,315,3,21,3,315,
%U A384665 1,45,3,105,3,315,1,63,1,105,3,315,1,315,3,15,3,63,1,315,3
%N A384665 Smallest odd multiplier k such that k*n is abundant.
%C A384665 a(n) <= 945 for all n. a(n) = 945 for prime numbers > 103.
%C A384665 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
%H A384665 Robert Israel, <a href="/A384665/b384665.txt">Table of n, a(n) for n = 1..10000</a>
%e A384665 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).
%p A384665 f:= proc(n) local k;
%p A384665   for k from 1 by 2 do if numtheory:-sigma(n*k) > 2*n*k then return k fi od
%p A384665 end proc:
%p A384665 map(f, [$1..100]); # _Robert Israel_, Jun 09 2025
%t A384665 a[n_] := Module[{k = 1}, While[DivisorSigma[-1, k*n] <= 2, k += 2]; k]; Array[a, 100] (* _Amiram Eldar_, Jun 06 2025 *)
%o A384665 (PARI) a(n) = my(k=1); while (sigma(k*n,-1)<=2, k+=2); k; \\ _Michel Marcus_, Jun 09 2025
%Y A384665 Cf. A005101, A005231, A023196, A254571.
%K A384665 nonn
%O A384665 1,1
%A A384665 _Sergio Pimentel_, Jun 06 2025