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

Author

Reinhard Zumkeller, Aug 25 2004

Keywords

• nonn

Examples

			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.
		

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

Crossrefs

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

Programs

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 *)