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A274355 Convolution of A048272 and A022567. 1
0, 1, 2, 5, 9, 15, 27, 42, 65, 99, 148, 214, 308, 435, 605, 839, 1145, 1548, 2080, 2769, 3659, 4812, 6278, 8145, 10518, 13506, 17257, 21961, 27821, 35095, 44117, 55243, 68928, 85735, 106285, 131357, 161893, 198944, 243817, 298060, 363446 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the convolution of A015723 and A000009.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Mircea Merca, Combinatorial interpretations of a recent convolution for the number of divisors of a positive integer, Journal of Number Theory, Volume 160, March 2016, Pages 60-75, corollary 3.5.

FORMULA

a(n) = Sum_{k=1..n} A048272(k)*A022567(n-k) = Sum_{k=0..n} A015723(k)*A000009(n-k).

a(n) ~ 3^(1/4) * log(2) * exp(Pi*sqrt(2*n/3)) / (2^(7/4) * Pi * n^(1/4)). - Vaclav Kotesovec, Oct 09 2018

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, add(add(d*[0, 1][1+

      irem(d, 2)], d=numtheory[divisors](j))*b(n-j), j=1..n)/n)

    end:

g:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, [1, 0],

      add((l->[l[1], l[2]+l[1]*j])(g(n-i*j, i-1)), j=0..min(n/i, 1))))

    end:

a:= n-> add(b(n-j)*g(j$2)[2], j=0..n):

seq(a(n), n=0..60);  # Alois P. Heinz, Jun 18 2016

MATHEMATICA

Table[Sum[Count[#, _?OddQ] - Count[#, _?EvenQ] &@ Divisors@ k SeriesCoefficient[QPochhammer[q, q^2]^-2, {q, 0, #}] &[n - k], {k, n}], {n, 0, 40}] (* Michael De Vlieger, Jun 18 2016, after Michael Somos at A022567 *)

CROSSREFS

Cf. A048272, A022567, A015723, A000009.

Sequence in context: A007176 A267757 A176691 * A054253 A045649 A267694

Adjacent sequences:  A274352 A274353 A274354 * A274356 A274357 A274358

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jun 18 2016

STATUS

approved

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Last modified March 26 04:32 EDT 2019. Contains 321481 sequences. (Running on oeis4.)