A349370 Dirichlet convolution of Kimberling's paraphrases (A003602) with itself.

1, 2, 4, 3, 6, 8, 8, 4, 14, 12, 12, 12, 14, 16, 28, 5, 18, 28, 20, 18, 38, 24, 24, 16, 35, 28, 48, 24, 30, 56, 32, 6, 58, 36, 60, 42, 38, 40, 68, 24, 42, 76, 44, 36, 108, 48, 48, 20, 66, 70, 88, 42, 54, 96, 92, 32, 98, 60, 60, 84, 62, 64, 148, 7, 108, 116, 68, 54, 118, 120, 72, 56, 74, 76, 176, 60, 126, 136, 80, 30

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = Sum_{d|n} A003602(n/d) * A003602(d).

Mathematica

k[n_] := (n / 2^IntegerExponent[n, 2] + 1)/2; a[n_] := DivisorSum[n, k[#] * k[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 16 2021 *)

Prog

(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
A349370(n) = sumdiv(n, d, A003602(n/d)*A003602(d));

Crossrefs

Cf. A347954, A347955, A347956, A349136, A349371, A349372, A349373, A349374, A349375, A349390, A349431, A349444, A349447 for Dirichlet convolutions of other sequences with A003602.

Sequence in context: A369825 A266411 A264740 * A137621 A242705 A350748

Adjacent sequences: A349367 A349368 A349369 * A349371 A349372 A349373

Keyword

nonn

Author

Antti Karttunen, Nov 15 2021

Status

approved