A078153 a(n) = A051201(n) - A000203(n).

0, 0, 0, 0, 2, 0, 5, 0, 6, 3, 10, 0, 15, 7, 9, 8, 22, 4, 24, 9, 21, 19, 32, 0, 35, 26, 30, 17, 44, 11, 52, 24, 41, 37, 45, 12, 66, 46, 52, 22, 71, 27, 80, 43, 52, 60, 85, 14, 89, 56, 79, 56, 101, 39, 89, 52, 94, 86, 117, 15, 122, 90, 85, 73, 118, 62, 139, 84, 116, 72, 145, 36

Offset: 1

Author

Labos Elemer, Nov 27 2002

Keywords

• nonn
• look

Examples

			n=15: sequence of D1 = {floor(15/j)} = {15,7,5,3,3,2,2,1,1,1,1,1,1,1,1}, Union(D1) = {15,7,5,3,2,1} = divisors(15) and {7,2}, a(15) = (15+7+5+3+2+1) - sigma(15) = 7 + 2 = 9.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051201, A000203, A055086, A000005, A078152, A076891.

Programs

Mathematica

Table[Apply[Plus, Union[Table[Floor[w/j], {j, 1, w}]]] -DivisorSigma[1, w], {w, 1, 128}]

PARI

a(n)=my(m=(sqrtint(4*n+1)-1)\2); m*(m+1)/2+sum(k=1, n\(m+1), n\k)-sigma(n) \\ Charles R Greathouse IV, Feb 14 2013