login
A353423
For even n, a(n) = -Sum_{d|n, d<n} a(n/2) * a(d), and for odd n, a(n) = a(A064989(n)), with a(1) = 1.
2
1, -1, -1, 0, -1, -1, -1, 0, 0, -1, -1, -2, -1, -1, -1, 0, -1, 0, -1, -2, -1, -1, -1, -8, 0, -1, 0, -2, -1, -5, -1, 0, -1, -1, -1, 0, -1, -1, -1, -8, -1, -5, -1, -2, -2, -1, -1, -96, 0, 0, -1, -2, -1, 0, -1, -8, -1, -1, -1, -70, -1, -1, -2, 0, -1, -5, -1, -2, -1, -5, -1, 0, -1, -1, 0, -2, -1, -5, -1, -96, 0, -1, -1, -70
OFFSET
1,12
COMMENTS
Apparently, for all i, j >= 1, A077462(i) = A077462(j) => a(i) = a(j).
FORMULA
a(p) = -1 for all primes p.
a(n) = a(A003961(n)) = a(A348717(n)), for all 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); };
memoA353423 = Map();
A353423(n) = if(1==n, 1, my(v); if(mapisdefined(memoA353423, n, &v), v, if(!(n%2), v = -sumdiv(n, d, if(d<n, A353423(n/2)*A353423(d), 0)), v = A353423(A064989(n))); mapput(memoA353423, n, v); (v)));
CROSSREFS
Cf. A070003 (positions of 0's), A167171 (positions of -1's), A096156 (positions of -2's), A007304 (positions of -5's), A086975 (positions of -70's), all these are so far conjectural. Also a subsequence of A178739 seems to give the positions of -96's.
Cf. also A353454, A353457, A353458, A353467 for similar recurrences.
Sequence in context: A374081 A353454 A276799 * A037907 A365167 A037801
KEYWORD
sign
AUTHOR
Antti Karttunen, Apr 21 2022
STATUS
approved