This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133725 #18 Jun 05 2025 00:42:07
%S A133725 1,4,11,17,34,35,69,70,105,106,175,142,246,213,284,284,424,321,531,
%T A133725 428,570,535,781,572,890,750,963,858,1246,860,1425,1144,1430,1288,
%U A133725 1716,1290,2034,1611,2004,1720,2500,1722,2751,2150,2580,2365,3289,2296,3507,2690
%N A133725 a(n) = Sum_{d|n} mu(n/d)*d*(3*d - 1)/2.
%C A133725 Previous name was: A054525 * A000326.
%C A133725 Möbius transform of the pentagonal numbers.
%F A133725 G.f.: Sum_{k>=1} mu(k) * x^k * (1 + 2*x^k) / (1 - x^k)^3. - _Ilya Gutkovskiy_, Sep 17 2021
%F A133725 a(n) = (3*A007434(n) - A000010(n))/2. - _Amiram Eldar_, Jun 04 2025
%e A133725 a(4) = 17 = (0, -1, 0, 1) dot (1, 5, 12, 22) = (0, -5, 0, 22).
%p A133725 read("transforms") : A000326 := proc(n) n*(3*n-1)/2 ; end: a000326 := [seq(A000326(n),n=1..300)] ; a133725 := MOBIUS(a000326) ; for i from 1 to nops(a133725) do printf("%d,",op(i,a133725)) ; od: # _R. J. Mathar_, Jan 19 2009
%t A133725 a[n_] := DivisorSum[n, #*(3*#-1) * MoebiusMu[n/#] &] / 2; Array[a, 50] (* _Amiram Eldar_, May 29 2025 *)
%o A133725 (PARI) a(n) = sumdiv(n, d, d*(3*d-1) * moebius(n/d)) / 2; \\ _Amiram Eldar_, May 29 2025
%Y A133725 Cf. A000010, A000326, A007434, A007438, A008683 (mu), A054525.
%K A133725 nonn
%O A133725 1,2
%A A133725 _Gary W. Adamson_, Sep 21 2007
%E A133725 More terms from _R. J. Mathar_, Jan 19 2009
%E A133725 New name from _Ilya Gutkovskiy_, Sep 17 2021