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

Author

Reinhard Zumkeller, Aug 25 2004

Keywords

• nonn

Examples

			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.
		

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

Crossrefs

Cf. A005101, A000041, A097798, A097799.

Programs

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 *)