cp's OEIS Frontend

A369761 The sum of divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.

%I A369761 #7 Feb 03 2024 10:16:24
%S A369761 1,3,4,7,6,12,8,31,13,18,12,28,14,24,24,31,18,39,20,42,32,36,24,124,
%T A369761 31,42,121,56,30,72,32,511,48,54,48,91,38,60,56,186,42,96,44,84,78,72,
%U A369761 48,124,57,93,72,98,54,363,72,248,80,90,60,168,62,96,104,511,84
%N A369761 The sum of divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.
%H A369761 Amiram Eldar, <a href="/A369761/b369761.txt">Table of n, a(n) for n = 1..10000</a>
%F A369761 a(n) = A000203(A356194(n)).
%F A369761 Multiplicative with a(p^e) = (p^(2^ceiling(log_2(e))+1)-1)/(p-1).
%F A369761 a(n) >= A000203(n), with equality if and only if n is in A138302.
%t A369761 f[p_, e_] := (p^(2^Ceiling[Log2[e]]+1)-1)/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A369761 (PARI) s(n) = {my(e=logint(n, 2)); if(n == 2^e, n, 2^(e+1))};
%o A369761 a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i,1]^(s(f[i,2])+1)-1)/(f[i,1]-1));}
%Y A369761 Cf. A000203, A138302, A353897, A356194, A369760, A369762.
%K A369761 nonn,easy,mult
%O A369761 1,2
%A A369761 _Amiram Eldar_, Jan 31 2024