login
A097797
Number of partitions of n into deficient numbers.
5
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 25 2004
STATUS
approved