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A108639
a(n) = Sum_{k=1..n} sigma_{n-k}(k), where sigma_m(k) = Sum_{j|k} j^m.
4
1, 3, 6, 13, 29, 77, 229, 771, 2863, 11573, 50365, 234161, 1156039, 6031751, 33130187, 190929778, 1151198268, 7243777234, 47462906927, 323188163753, 2282922216819, 16701529748621, 126359471558613, 987316752551419
OFFSET
1,2
COMMENTS
Row sums of number triangle A109974. - Paul Barry, Jul 06 2005
LINKS
EXAMPLE
a(5) = 1^4 + (1^3 + 2^3) + (1^2 + 3^2) + (1^1 + 2^1 + 4^1) + (1^0 + 5^0) = 1 + 1 + 8 + 1 + 9 + 1 + 2 + 4 + 1 + 1 = 29.
MAPLE
with(numtheory): s:=proc(n, k) local div: div:=divisors(n): sum(div[j]^k, j=1..tau(n)) end: a:=n->sum(s(i, n-i), i=1..n): seq(a(n), n=1..27); # Emeric Deutsch, Jul 13 2005
MATHEMATICA
Array[Sum[DivisorSigma[# - k, k], {k, #}] &, 24] (* Michael De Vlieger, Dec 23 2017 *)
PROG
(PARI) a(n) = sum(k=1, n, sigma(k, n-k)); \\ Michel Marcus, Dec 24 2017
(Magma)
A108639:= func< n | (&+[DivisorSigma(j, n-j): j in [0..n-1]]) >;
[A108639(n): n in [1..30]]; // G. C. Greubel, Oct 18 2023
(SageMath)
def A108639(n): return sum(sigma(n-j, j) for j in range(n))
[A108639(n) for n in range(1, 31)] # G. C. Greubel, Oct 18 2023
CROSSREFS
Cf. A109974, A245466 (with k instead of n-k).
Sequence in context: A093128 A005313 A213674 * A327795 A087218 A098075
KEYWORD
nonn
AUTHOR
Leroy Quet, Jul 06 2005
EXTENSIONS
More terms from Emeric Deutsch, Jul 13 2005
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007
STATUS
approved