A353454 a(1) = 1, for n > 1, a(n) = -Sum_{d|n, dA064989(n)) * a(d).

1, -1, 1, 0, -1, 1, 1, 0, 0, 1, -1, 2, 1, 1, -1, 0, -1, 0, 1, 0, -3, 1, -1, 4, 0, 1, 0, 2, 1, -1, -1, 0, -1, 1, 1, 0, 1, 1, -3, 0, -1, -1, 1, 0, 0, 1, -1, 8, 0, 0, -1, 2, 1, 0, -3, 4, -3, 1, -1, -2, 1, 1, 0, 0, 1, -1, -1, 0, -1, 3, 1, 0, -1, 1, 0, 2, -1, -1, 1, 0, 0, 1, -1, -4, -3, 1, -3, 0, 1, 0, 9, 0, -1, 1, 1, 16

Offset: 1

Author

Antti Karttunen, Apr 21 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000040, A064989, A353455 [= a(A064989(n))].

Cf. also A353423, A353457.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A064989(n) = { my(f=factor(A000265(n))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
memoA353454 = Map();
A353454(n) = if(1==n,1,my(v); if(mapisdefined(memoA353454,n,&v), v, v = -sumdiv(n,d,if(dA353454(A064989(n))*A353454(d),0)); mapput(memoA353454,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA353455(n) * a(d).

For all n >= 1, a(A000040(n)) = ((-1)^n).