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A327327
Partial sums of the sum of nonpowers of 2 dividing n.
1
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.
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.
Sequence in context: A300367 A296106 A329094 * A370640 A328976 A059197
KEYWORD
nonn
AUTHOR
Omar E. Pol, Sep 14 2019
STATUS
approved