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Sums of odd numbers, omitting squares.
1

%I #29 Jul 05 2022 07:17:04

%S 3,8,15,26,39,54,71,90,111,134,161,190,221,254,289,326,365,406,449,

%T 494,541,592,645,700,757,816,877,940,1005,1072,1141,1212,1285,1360,

%U 1437,1516,1599,1684,1771,1860,1951,2044,2139,2236,2335,2436,2539,2644,2751

%N Sums of odd numbers, omitting squares.

%C Partial sums of A088828.

%H G. C. Greubel, <a href="/A159465/b159465.txt">Table of n, a(n) for n = 1..5000</a>

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

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

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

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

%o (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

%Y Cf. A088828, A014105.

%K nonn,easy

%O 1,1

%A _Gerald Hillier_, Apr 13 2009

%E More terms from _Klaus Brockhaus_ and _R. J. Mathar_, Apr 16 2009

%E Name and comment swapped by _Michel Marcus_, Mar 31 2020