A097800 Number of partitions of the n-th abundant number into abundant numbers.

1, 1, 1, 2, 2, 4, 2, 4, 7, 8, 5, 14, 14, 5, 23, 26, 18, 38, 17, 46, 65, 34, 75, 50, 106, 59, 125, 175, 203, 275, 326, 243, 434, 519, 675, 477, 806, 1044, 1244, 985, 1604, 1902, 2420, 1892, 2887, 2391, 3632, 2932, 4342, 5424, 4509, 6460, 5513, 8021, 9557, 11817

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Abundant Number

Eric Weisstein's World of Mathematics, Partition

Example

a(8)=4: A005101(8)=42 = A005101(5)+A005101(1)=30+12 =
A005101(4)+A005101(2)=24+18 = A005101(2)+2*A005101(1)=18+12+12.

Mathematica

n = 245; d = Select[Range[n], DivisorSigma[1, #] > 2 # &]; CoefficientList[ Series[1/Product[1 - x^d[[i]], {i, 1, Length[d]}], {x, 0, n}], x][[d + 1]] (* Amiram Eldar, Aug 02 2019 *)

Crossrefs

Cf. A005101, A000041, A097798, A097799.

Sequence in context: A222153 A219403 A219451 * A183402 A217839 A083779

Adjacent sequences: A097797 A097798 A097799 * A097801 A097802 A097803

Keyword

nonn

Author

Reinhard Zumkeller, Aug 25 2004

Status

approved