A097797 - OEIS

%I #7 Aug 02 2019 12:58:52

%S 1,2,3,5,7,10,14,20,27,37,49,65,85,111,143,184,234,297,374,469,585,

%T 727,899,1108,1360,1664,2028,2464,2985,3606,4343,5218,6252,7474,8913,

%U 10605,12591,14918,17639,20816,24519,28829,33836,39646,46377,54165,63162

%N Number of partitions of n into deficient numbers.

%H Amiram Eldar, <a href="/A097797/b097797.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DeficientNumber.html">Deficient Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Partition.html">Partition</a>

%e 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.

%t 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 *)

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

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Aug 25 2004