cp's OEIS Frontend

A373113 For n >= 1, a(n) = Sum_{i = n..(n + A000005(n) - 1)} i.

%I A373113 #11 May 28 2024 06:48:12
%S A373113 1,5,7,15,11,30,15,38,30,46,23,87,27,62,66,90,35,123,39,135,90,94,47,
%T A373113 220,78,110,114,183,59,268,63,207,138,142,146,360,75,158,162,348,83,
%U A373113 364,87,279,285,190,95,525,150,315,210,327,107,460,226,476,234,238,119,786,123
%N A373113 For n >= 1, a(n) = Sum_{i = n..(n + A000005(n) - 1)} i.
%C A373113 A005385 is a subsequence.
%F A373113 a(n) = A066446(n) + n*A000005(n).
%F A373113 a(n) = A000005(n)*(A000005(n) - 1)/2 + n*A000005(n).
%e A373113 n = 4: A000005(4) = 3, 4 + 5 + 6 = 15, thus a(4) = 15.
%e A373113 n = 5: A000005(5) = 2, 5 + 6 = 11, thus a(5) = 11.
%e A373113 n = 6: A000005(6) = 4, 6 + 7 + 8 + 9 = 30, thus a(6) = 30.
%t A373113 a[n_] := Module[{d = DivisorSigma[0, n]}, d*(d-1)/2 + n*d]; Array[a, 60] (* _Amiram Eldar_, May 25 2024 *)
%o A373113 (PARI) a(n) = my(d=numdiv(n)); n*d + d*(d-1)/2; \\ _Michel Marcus_, May 28 2024
%Y A373113 Cf. A000005, A005384, A005385, A066446.
%K A373113 nonn
%O A373113 1,2
%A A373113 _Ctibor O. Zizka_, May 25 2024