A324542 Möbius transform of A324118, where A324118(n) = A000593(A156552(n)).

0, 1, 1, 3, 1, 4, 1, 4, 3, 11, 1, 3, 1, 16, 4, 16, 1, 5, 1, 4, 11, 46, 1, 8, 3, 82, 4, 27, 1, 10, 1, 8, 16, 174, 4, 20, 1, 256, 46, 32, 1, 4, 1, 17, 3, 798, 1, 8, 3, 15, 82, 45, 1, 12, 11, 20, 174, 1300, 1, 2, 1, 2734, 4, 72, 16, 27, 1, 125, 256, 8, 1, 20, 1, 4354, 5, 363, 4, 25, 1, 8, 16, 10926, 1, 53, 46, 20518, 798, 168, 1, 35, 11, 317

Offset: 1

Author

Antti Karttunen, Mar 07 2019

Keywords

• sign

Comments

The first three zeros after a(1) occur at n = 192, 288, 3645.

The first negative term is a(150) = -1. There are 184 negative terms among the first 4473 terms.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4473
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000593, A008683, A156552, A324118, A324543.

Cf. also A322993, A322994.

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)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
A322993(n) = A156552(2*A246277(n));
memoA324118 = Map();
A324118(n) = if(1==n, 0, my(v); if(mapisdefined(memoA324118,n,&v), v, v=sigma(A322993(n)); mapput(memoA324118,n,v); (v)));
A324542(n) = sumdiv(n,d,moebius(n/d)*A324118(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A324118(d).