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A097798 Number of partitions of n into abundant numbers. 4
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 4, 0, 1, 0, 2, 0, 4, 0, 2, 0, 0, 0, 7, 0, 2, 0, 2, 0, 8, 0, 5, 0, 2, 0, 14, 0, 4, 0, 4, 0, 14, 0, 8, 0, 5, 0, 23, 0, 9, 0, 9, 0, 26, 0, 18, 0, 9, 0, 38, 0, 16, 0, 17, 0, 46, 0, 29, 0, 19, 0, 65, 0, 32, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,25

COMMENTS

n = 977 = 945 + 32 is the first prime for which sequence obtains a nonzero value, as a(977) = a(32) = 1. 945 is the first term in A005231. - Antti Karttunen, Sep 06 2018

a(n) = 0 for 496 values of n, the largest of which is 991 (see A283550). - David A. Corneth, Sep 08 2018

LINKS

David A. Corneth, Table of n, a(n) for n = 0..10000 (a(1) through a(532) by Antti Karttunen)

David A. Corneth, PARI program

Eric Weisstein's World of Mathematics, Abundant Number

Eric Weisstein's World of Mathematics, Partition

PROG

(PARI)

abundants_up_to_reversed(n) = { my(s = Set([])); for(k=1, n, if(sigma(k)>(2*k), s = setunion([k], s))); vecsort(s, , 4); };

partitions_into(n, parts, from=1) = if(!n, 1, my(k = #parts, s=0); for(i=from, k, if(parts[i]<=n, s += partitions_into(n-parts[i], parts, i))); (s));

A097798(n) = partitions_into(n, abundants_up_to_reversed(n)); \\ Antti Karttunen, Sep 06 2018

(PARI) \\ see Corneth link

CROSSREFS

Cf. A005101, A005231, A000041, A097800, A097797, A097796, A097795.

Cf. also A066874, A282568, A283550.

Sequence in context: A143840 A028649 A305558 * A065205 A036272 A257403

Adjacent sequences:  A097795 A097796 A097797 * A097799 A097800 A097801

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 25 2004

EXTENSIONS

a(0) = 1 prepended by David A. Corneth, Sep 08 2018

STATUS

approved

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Last modified June 18 07:37 EDT 2019. Contains 324203 sequences. (Running on oeis4.)