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Search: id:A110412
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| A110412 |
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Sum_{d<n is a divisor of n} tau(n-d). |
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+0
3
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| 0, 1, 2, 4, 3, 7, 4, 9, 8, 9, 4, 17, 6, 10, 14, 18, 5, 20, 6, 21, 16, 12, 4, 33, 14, 13, 18, 24, 6, 33, 8, 29, 18, 12, 18, 44, 9, 13, 17, 41, 8, 37, 8, 26, 39, 14, 4, 57, 18, 30, 20, 28, 6, 41, 20, 45, 20, 14, 4, 68, 12, 16, 40, 46, 25, 43, 8, 25, 18, 44, 8, 80, 12, 16, 42, 30, 22, 42, 8
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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It appears that a(n) > tau(n) for n >= 4.
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EXAMPLE
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a(9)=tau(9-1)+tau(9-3)=tau(8)+tau(6)=4+4=8.
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MAPLE
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with(numtheory): a:=proc(n) local div: div:=divisors(n): sum(tau(n-div[j]), j=1..tau(n)-1): end: seq(a(n), n=2..90); (Deutsch)
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MATHEMATICA
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f[n_] := Plus @@ (DivisorSigma[0, n - # ] & /@ Most[Divisors[n]]); Table[ f[n], {n, 79}] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A007425.
Sequence in context: A051851 A011171 A007203 this_sequence A064357 A120619 A084385
Adjacent sequences: A110409 A110410 A110411 this_sequence A110413 A110414 A110415
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 31 2005
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EXTENSIONS
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Edited, corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 05 2005
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