OFFSET
2,7
LINKS
Antti Karttunen, Table of n, a(n) for n = 2..6381 (based on Hans Havermann's factorization of A156552)
FORMULA
PROG
(PARI)
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};
A329697(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A329697(f[k, 1]-1)))); };
(PARI)
\\ Version using the factorization file available at https://oeis.org/A156552/a156552.txt
v156552sigs = readvec("a156552.txt");
A329697(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A329697(f[k, 1]-1)))); };
A342651(n) = if(isprime(n), 0, my(prsig=v156552sigs[n], ps=prsig[1], es=prsig[2]); sum(i=2-(ps[1]%2), #ps, es[i]*(1+A329697(ps[i]-1)))); \\ Antti Karttunen, Jan 29 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 18 2021
STATUS
approved