A279910 a(n) = Sum_{k=1..n} prime(k+1)*floor(n/prime(k+1)).

0, 0, 3, 3, 8, 11, 18, 18, 21, 26, 37, 40, 53, 60, 68, 68, 85, 88, 107, 112, 122, 133, 156, 159, 164, 177, 180, 187, 216, 224, 255, 255, 269, 286, 298, 301, 338, 357, 373, 378, 419, 429, 472, 483, 491, 514, 561, 564, 571, 576, 596, 609, 662, 665, 681, 688, 710, 739, 798, 806, 867, 898, 908, 908, 926, 940, 1007, 1024, 1050, 1062

Offset: 1

Author

Ilya Gutkovskiy, Dec 24 2016

Keywords

• nonn
• easy

Comments

Sum of all odd prime divisors of all positive integers <= n.

Examples

			For n = 7 the odd prime divisors of the first seven positive integers are {0}, {0}, {3}, {0}, {5}, {3}, {7} so a(7) = 0 + 0 + 3 + 0 + 5 + 3 + 7 = 18.
		

Links

• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A005069, A008472, A024924, A052928.

Programs

Mathematica

Table[Sum[Prime[k + 1] Floor[n/Prime[k + 1]], {k, 1, n}], {n, 70}]
Rest[nmax = 70; CoefficientList[Series[(1/(1 - x)) Sum[Prime[k] x^Prime[k]/(1 - x^Prime[k]), {k, 2, nmax}], {x, 0, nmax}], x]]

Formula

G.f.: (1/(1 - x))*Sum_{k>=2} prime(k)*x^prime(k)/(1 - x^prime(k)).

a(n) = -2*floor(n/2) + Sum_{k=1..n} prime(k)*floor(n/prime(k)) .

a(n) = A024924(n) - A052928(n).