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

1,3

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.

Links

Table of n, a(n) for n=1..60.

Formula

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

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

Example

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.

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 *)

Crossrefs

Partial sums of A326988.

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

Sequence in context: A300367 A296106 A329094 * A370640 A328976 A059197

Adjacent sequences: A327324 A327325 A327326 * A327328 A327329 A327330

Keyword

nonn

Author

Omar E. Pol, Sep 14 2019

Status

approved