A319687 a(n) = A318509(n) - A002487(n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 6, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, -6, 0, -4, 0, 0, 0, -4, 0, -6, 0, 10, 0, 0, 0, 4, 2, 0, -2, 0, 0, 0

Offset

1,15

Comments

All terms seem to be even. See the conjecture given in A261179.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to Stern's sequences

Formula

a(n) = A318509(n) - A002487(n).

Prog

(PARI)
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A318509(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = A002487(f[i, 1])); factorback(f); };
A319687(n) = (A318509(n) - A002487(n));
(Python)
from math import prod
from functools import reduce
from sympy import factorint
def A319687(n): return prod(sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(p)[-1:2:-1], (1, 0)))**e for p, e in factorint(n).items())-sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(n)[-1:2:-1], (1, 0))) # Chai Wah Wu, May 18 2023

Crossrefs

Cf. A002487, A261179, A317837, A318509, A323365.

Sequence in context: A350139 A293814 A045837 * A374217 A126825 A045833

Adjacent sequences: A319684 A319685 A319686 * A319688 A319689 A319690

Keyword

sign,look

Author

Antti Karttunen, Oct 02 2018

Status

approved