A349371 Inverse Möbius transform of Kimberling's paraphrases (A003602).

1, 2, 3, 3, 4, 6, 5, 4, 8, 8, 7, 9, 8, 10, 14, 5, 10, 16, 11, 12, 18, 14, 13, 12, 17, 16, 22, 15, 16, 28, 17, 6, 26, 20, 26, 24, 20, 22, 30, 16, 22, 36, 23, 21, 42, 26, 25, 15, 30, 34, 38, 24, 28, 44, 38, 20, 42, 32, 31, 42, 32, 34, 55, 7, 44, 52, 35, 30, 50, 52, 37, 32, 38, 40, 65, 33, 50, 60, 41, 20, 63, 44, 43

Offset

1,2

Comments

Dirichlet convolution of sigma (A000203) with A349431, or equally, A264740 with A349447. - Antti Karttunen, Nov 21 2021

Links

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

Formula

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

a(n) = Sum_{d|n} A000203(n/d)*A349431(d) = Sum_{d|n} A264740(n/d)*A349447(d). - Antti Karttunen, Nov 21 2021

Mathematica

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

Prog

(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
A349371(n) = sumdiv(n, d, A003602(d));

Crossrefs

Cf. A000203, A264740.

Cf. also A347954, A347955, A347956, A349136, A349370, A349372, A349373, A349374, A349375, A349390, A349431, A349444, A349447 for Dirichlet convolutions of other sequences with A003602.

Cf. also A349393.

Sequence in context: A159999 A003977 A003971 * A282442 A200668 A200469

Adjacent sequences: A349368 A349369 A349370 * A349372 A349373 A349374

Keyword

nonn

Author

Antti Karttunen, Nov 15 2021

Status

approved