cp's OEIS Frontend

A385645 a(n) is the number of distinct sums of distinct prime powers dividing n.

%I A385645 #8 Jul 15 2025 17:04:53
%S A385645 1,3,3,7,3,6,3,15,7,7,3,10,3,7,7,31,3,13,3,12,7,7,3,18,7,7,15,14,3,11,
%T A385645 3,63,7,7,7,19,3,7,7,20,3,13,3,15,14,7,3,34,7,15,7,15,3,27,7,22,7,7,3,
%U A385645 15,3,7,14,127,7,13,3,15,7,13,3,27,3,7,15,15,7,13
%N A385645 a(n) is the number of distinct sums of distinct prime powers dividing n.
%H A385645 Felix Huber, <a href="/A385645/b385645.txt">Table of n, a(n) for n = 1..10000</a>
%F A385645 a(p) = 3 for prime p.
%F A385645 a(p^k) = A119347(p^k) for prime p and nonnegative integer k.
%F A385645 A385646(n) < a(n) <= A119347(n).
%e A385645 The a(4) = 7 distinct sums of distinct prime powers dividing 4 are 1, 2, 4, 1 + 2, 1 + 4, 2 + 4 and 1 + 2 + 4.
%p A385645 A385645:=proc(n)
%p A385645     local b,k,l,i,j;
%p A385645     l:=[1,seq(seq(i[1]^j,j=1..i[2]),i in ifactors(n)[2])]:
%p A385645     b:=proc(m,i)
%p A385645         option remember;
%p A385645         `if`(m=0,1,`if`(i<1,0,b(m,i-1)+`if`(l[i]>m,0,b(m-l[i],i-1))))
%p A385645     end;
%p A385645     return nops(select(x->x>0,[seq(b(k,nops(l)),k=1..add(l))]))
%p A385645     end:
%p A385645 seq(A385645(n),n=1..78);
%Y A385645 Cf. A000040, A000961, A119347, A385646.
%K A385645 nonn,easy
%O A385645 1,2
%A A385645 _Felix Huber_, Jul 11 2025