A327327 Partial sums of the sum of nonpowers of 2 dividing n.

0, 0, 3, 3, 8, 17, 24, 24, 36, 51, 62, 83, 96, 117, 140, 140, 157, 193, 212, 247, 278, 311, 334, 379, 409, 448, 487, 536, 565, 634, 665, 665, 712, 763, 810, 894, 931, 988, 1043, 1118, 1159, 1252, 1295, 1372, 1449, 1518, 1565, 1658, 1714, 1804, 1875, 1966, 2019, 2136, 2207, 2312, 2391, 2478, 2537, 2698

Offset: 1

Author

Omar E. Pol, Sep 14 2019

Keywords

• nonn

Comments

a(n) can be represented with a diagram since the symmetric diagram of A024916(n) is greater than or equal to the diagram of A080277(n). The difference between both diagrams is a representation of a(n). For more information about the symmetric diagram of A024916 see A236104 and A237593.

Examples

			The divisors of 6 are 1, 2, 3, 6. But 1 and 2 are powers of 2, so we only add up 3, 6 to get 9, and add that to the running total of 8 to get a(6) = 17.
		

Crossrefs

Partial sums of A326988.

Cf. A000203, A024916, A038712, A080277, A236104, A237593, A327326.

Programs

Mathematica

Accumulate[Table[DivisorSigma[1, n] - Denominator[DivisorSigma[1, 2n]/DivisorSigma[1, n]], {n, 100}]] (* Alonso del Arte, Nov 18 2019, based on Wesley Ivan Hurt's program for A326988 *)

Formula

a(n) = A024916(n) - A080277(n).

a(n) = a(n-1) when n is a power of 2.