The On-Line Encyclopedia of Integer Sequences (OEIS)

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A139055

Sum of proper divisors of the number of partitions of n.
(history; published version)

#10 by Susanna Cuyler at Tue Jan 07 09:07:40 EST 2020

STATUS

proposed

approved

#9 by Michel Marcus at Tue Jan 07 08:27:31 EST 2020

STATUS

editing

proposed

#8 by Michel Marcus at Tue Jan 07 08:27:26 EST 2020

PROG

(PARI) a(n) = my(p=numbpart(n)); sigma(p) - p; \\ Michel Marcus, Jan 07 2020

STATUS

proposed

editing

#7 by Amiram Eldar at Tue Jan 07 07:53:41 EST 2020

STATUS

editing

proposed

#6 by Amiram Eldar at Tue Jan 07 07:50:17 EST 2020

MATHEMATICA

s[n_] := DivisorSigma[1, n] - n; Array[s[PartitionsP[#]] &, 50] (* Amiram Eldar, Jan 07 2020 *)

#5 by Amiram Eldar at Tue Jan 07 07:42:59 EST 2020

LINKS

Amiram Eldar, <a href="/A139055/b139055.txt">Table of n, a(n) for n = 1..10000</a> (calculated from the b-file files at A000041 and A001065)

#4 by Amiram Eldar at Tue Jan 07 07:42:39 EST 2020

LINKS

Amiram Eldar, <a href="/A139055/b139055.txt">Table of n, a(n) for n = 1..10000</a> (calculated from the b-file at A000041 and A001065)

#3 by Amiram Eldar at Tue Jan 07 07:41:56 EST 2020

LINKS

Amiram Eldar, <a href="/A139055/b139055.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 17:33:54 EDT 2012

AUTHOR

_Omar E. Pol (info(AT)polprimos.com), _, Apr 16 2008

Discussion

Fri Mar 30

17:33

OEIS Server: https://oeis.org/edit/global/157

#1 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

NAME

Sum of proper divisors of the number of partitions of n.

DATA

0, 1, 1, 1, 1, 1, 9, 14, 42, 54, 64, 19, 1, 105, 196, 153, 183, 191, 536, 333, 1548, 1014, 257, 1649, 1282, 4284, 3326, 2870, 1483, 7500, 4390, 4419, 7641, 9866, 7461, 1, 5435, 9097, 38511, 50214, 29913, 33874, 41283, 22041, 47954, 109338, 107806, 77175, 61579, 129998

OFFSET

1,7

FORMULA

a(n) = A001065(A000041(n)).

EXAMPLE

a(7) = 9 because the number of partitions of 7 is 15 and the sum of proper divisors of 15 is equal to 1 + 3 + 5 = 9.

CROSSREFS

Cf. A000041, A001065, A139041.

KEYWORD

nonn

AUTHOR

Omar E. Pol (info(AT)polprimos.com), Apr 16 2008

STATUS

approved