A339896 a(n) = A056239(n) - A339894(n).

0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 1, 1, 1, 0, 2, 2, 1, 2, 1, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 2, 2, 2, 1, 1, 0, 2, 2, 2, 1, 1, 0, 2, 0, 1, 2, 3, 2, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 2, 2, 0, 2, 3, 1, 0, 2, 2, 1, 1, 2, 0, 2, 2, 1, 1, 1, 2, 3, 0, 2, 2, 3, 0, 2, 0, 2, 2

Offset: 1

Author

Antti Karttunen, Dec 21 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000523, A056239, A122111, A334201, A339823, A339894, A339895.

Programs

PARI

A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
A339896(n) = (A056239(n)-A000523(A122111(n)));

Formula

a(n) = A056239(n) - A339894(n).

a(n) = A334201(n) - A339895(n).

a(n) = A339823(A122111(n)).