A353455 a(n) = A353454(A064989(n)).

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

Offset

1,45

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from indices in prime factorization

Formula

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

Prog

(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(d<n, A353454(A064989(n))*A353454(d), 0)); mapput(memoA353454, n, v); (v)));
A353455(n) = A353454(A064989(n));

Crossrefs

Cf. A000040, A064989, A353454.

Cf. also A353458.

Sequence in context: A255319 A214088 A005091 * A276516 A346100 A253638

Adjacent sequences: A353452 A353453 A353454 * A353456 A353457 A353458

Keyword

sign

Author

Antti Karttunen, Apr 21 2022

Status

approved