cp's OEIS Frontend

A129501 A103994 * A115361.

%I A129501 #14 Sep 24 2019 02:39:49
%S A129501 1,2,1,-1,0,1,3,2,0,1,-1,0,0,0,1,-2,-1,2,0,0,1,-1,0,0,0,0,0,1,4,3,0,2,
%T A129501 0,0,0,1,0,0,-1,0,0,0,0,0,1,-2,-1,0,0,2,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,
%U A129501 0,1,-3,-2,3,-1,0,2,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,1
%N A129501 A103994 * A115361.
%C A129501 Row sums = A129502: (1, 3, 0, 6, 0, 0, 0, 10, 0, 0, ...).
%H A129501 Andrew Howroyd, <a href="/A129501/b129501.txt">Table of n, a(n) for n = 1..1275</a>
%F A129501 A103994 * A115361 as infinite lower triangular matrices.
%F A129501 T(n,k) = A317673(n/k) for k | n, T(n,k) = 0 otherwise. - _Andrew Howroyd_, Aug 03 2018
%e A129501 First few rows of the triangle are:
%e A129501    1;
%e A129501    2,  1;
%e A129501   -1,  0,  1;
%e A129501    3,  2,  0,  1;
%e A129501   -1,  0,  0,  0,  1;
%e A129501   -2, -1,  2,  0,  0,  1;
%e A129501   -1,  0,  0,  0,  0,  0,  1;
%e A129501    4,  3,  0,  2,  0,  0,  0,  1;
%e A129501    0,  0, -1,  0,  0,  0,  0,  0,  1;
%e A129501   ...
%t A129501 b[n_] := Module[{e}, Sum[e = IntegerExponent[d, 2]; If[d == 2^e, MoebiusMu[n/d] Binomial[2 + e, 2], 0], {d, Divisors[n]}]];
%t A129501 T[n_, k_] := If[Divisible[n, k], b[n/k], 0];
%t A129501 Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 24 2019 *)
%o A129501 (PARI) T(n,k)={ if(n%k, 0, sumdiv(n/k, d, my(e=valuation(d, 2)); if(d==1<<e, moebius(n/(k*d))*binomial(2+e,2), 0))) } \\ _Andrew Howroyd_, Aug 03 2018
%Y A129501 Column 1 is A317673 (Moebius transform of A129502).
%Y A129501 Row sums are A129502.
%Y A129501 Cf. A103994, A115361, A129360, A000217, A001511.
%K A129501 tabl,sign
%O A129501 1,2
%A A129501 _Gary W. Adamson_, Apr 17 2007
%E A129501 Terms a(56) and beyond from _Andrew Howroyd_, Aug 03 2018