A324574 a(1) = 0; for n > 1, a(n) = A033879(A087207(n)).

0, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 5, 0, 1, 1, 2, 1, 4, 2, 16, 1, 2, 1, 18, 1, 5, 1, 6, 1, 1, -3, 46, -4, 2, 1, 82, 14, 4, 1, 10, 1, 16, 0, 256, 1, 2, 1, 4, -12, 18, 1, 2, -2, 5, 8, 226, 1, 6, 1, 748, 2, 1, -19, 18, 1, 46, -12, 12, 1, 2, 1, 1362, 0, 82, -12, 22, 1, 4, 1, 3838, 1, 10, 10, 5458, 254, 16, 1, 6, -10, 256, -348, 12250

Offset

1,6

Comments

As A087207 is a surjective function that toggles the parity, it follows that if it can be proved/disproved that a(n) = 0 for some/any even n, then it also proves/disproves the existence of odd perfect numbers.

The positions (n > 1) of zeros in squarefree n, 15, 385, ..., can be obtained as A019565(A000396(n)).

Links

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

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(1) = 0; for n > 1, a(n) = A033879(A087207(n)).

a(n) = a(A007947(n)) = A324575(A007947(n)).

Prog

(PARI)
A033879(n) = (2*n-sigma(n));
A087207(n) = vecsum(apply(p->1<<primepi(p-1), factor(n)[, 1])); \\ From A087207
A324574(n) = if(1==n, 0, A033879(A087207(n)));

Crossrefs

Cf. A000396, A007947, A033879, A019565, A087207, A324573, A324575.

Cf. also A323244, A323174, A324546.

Sequence in context: A139320 A174204 A118106 * A143201 A340082 A348647

Adjacent sequences: A324571 A324572 A324573 * A324575 A324576 A324577

Keyword

sign

Author

Antti Karttunen, Mar 08 2019

Status

approved