A374215 a(n) = A347381(n) - A374214(n).

0, 0, 1, 1, 1, 0, 3, 2, 1, 3, 3, 2, 2, 3, 0, 3, 6, 3, 5, 1, 3, 5, 7, 2, 2, 4, 2, 0, 8, 4, 10, 4, 3, 7, 1, 4, 4, 7, 2, 4, 10, 4, 9, 4, 2, 9, 13, 4, 1, 4, 6, 7, 15, 4, 4, 5, 5, 9, 15, 4, 7, 10, 2, 5, 3, 6, 12, 6, 7, 5, 19, 5, 9, 6, 3, 8, 0, 5, 19, 4, 2, 11, 20, 4, 6, 11, 8, 6, 22, 4, 2, 8, 10, 15, 6, 5, 24, 5, 2, 5, 20

Offset: 1

Author

Antti Karttunen, Jul 07 2024

Keywords

• sign

Comments

The first negative term is a(1271) = A347381(1271) - A374214(1271) = 9 - 10 = -1. The next ones occur at n=97969, 133907, 142859, 161257, 189209.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A005940, A347381, A374214, A374218 (indices of nonpositive terms).

Programs

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A252463(n) = if(!(n%2),n/2,A064989(n));
A347381(n) = if(1==n,0, my(lista=List([]), i, k=n, stemvec, stemlen, sbr=sigma(n)); while(k>1, listput(lista,k); k = A252463(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,sbr))>0, return(stemlen-i)); sbr = A252463(sbr)));
A374214(n) = { my(m=-1,x); fordiv(n,d,if(d>1 && dA347381(d); if(m<0 || xA374215(n) = (A347381(n)-A374214(n));