A097797 Number of partitions of n into deficient numbers.

1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 65, 85, 111, 143, 184, 234, 297, 374, 469, 585, 727, 899, 1108, 1360, 1664, 2028, 2464, 2985, 3606, 4343, 5218, 6252, 7474, 8913, 10605, 12591, 14918, 17639, 20816, 24519, 28829, 33836, 39646, 46377, 54165, 63162

Offset

1,2

Links

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

Eric Weisstein's World of Mathematics, Deficient Number

Eric Weisstein's World of Mathematics, Partition

Example

n=10: 6 is the only non-deficient number <= 10 and five partitions of 10 contain 6 as part: 6 + 4 = 6 + 3 + 1 = 6 + 2 + 2 = 6 + 2 + 1 + 1 = 6 + 1 + 1 + 1 + 1, therefore a(10) = A000041(10) - 5 = 42 - 5 = 37.

Mathematica

n = 50; d = Select[Range[n], DivisorSigma[1, #] < 2 # &]; Rest@CoefficientList[ Series[1/Product[1 - x^d[[i]], {i, 1, Length[d]}], {x, 0, n}], x] (* Amiram Eldar, Aug 02 2019 *)

Crossrefs

Cf. A005100, A000041, A097799, A097798, A097796, A097795.

Sequence in context: A123630 A326977 A035967 * A219601 A035975 A035984

Adjacent sequences: A097794 A097795 A097796 * A097798 A097799 A097800

Keyword

nonn

Author

Reinhard Zumkeller, Aug 25 2004

Status

approved