A159465 Sums of odd numbers, omitting squares.

3, 8, 15, 26, 39, 54, 71, 90, 111, 134, 161, 190, 221, 254, 289, 326, 365, 406, 449, 494, 541, 592, 645, 700, 757, 816, 877, 940, 1005, 1072, 1141, 1212, 1285, 1360, 1437, 1516, 1599, 1684, 1771, 1860, 1951, 2044, 2139, 2236, 2335, 2436, 2539, 2644, 2751

Offset

1,1

Comments

Partial sums of A088828.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n) = (n+S)^2 - (4*S^3-S)/3 where S = ceiling(round(sqrt(2*n-1))/2).

a(n) = n^2 + 2*(n + Sum_{i=1..n} max(0, n - A014105(i))). - John Tyler Rascoe, Jul 04 2022

Example

a(5) = 3 + 5 + 7 + 11 + 13 = 39.

Mathematica

s = Select[Range[1, 200, 2], EvenQ[DivisorSigma[1, #] - 2 #] &]; Accumulate[s] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)

Prog

(Magma) S:=[ n: n in [1..108 by 2] | IsEven(SumOfDivisors(n)-2*n) ]; [ n eq 1 select S[1] else Self(n-1)+S[n]: n in [1..#S] ]; // Klaus Brockhaus, Apr 15 2009

Crossrefs

Cf. A088828, A014105.

Sequence in context: A071399 A387529 A001208 * A071148 A172289 A172296

Adjacent sequences: A159462 A159463 A159464 * A159466 A159467 A159468

Keyword

nonn,easy

Author

Gerald Hillier, Apr 13 2009

Extensions

More terms from Klaus Brockhaus and R. J. Mathar, Apr 16 2009

Name and comment swapped by Michel Marcus, Mar 31 2020

Status

approved