cp's OEIS Frontend

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.

A003970 Möbius transform of A003960 (with alternating zeros omitted).

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%I A003970 #28 Nov 03 2023 11:21:35
%S A003970 1,1,2,3,2,5,6,2,8,9,3,11,6,4,14,15,5,6,18,6,20,21,4,23,12,8,26,10,9,
%T A003970 29,30,6,12,33,11,35,36,6,15,39,8,41,16,14,44,18,15,18,48,10,50,51,6,
%U A003970 53,54,18,56,22,12,24,30,20,18,63,21,65,27,8,68,69,23,30,28,12,74,75
%N A003970 Möbius transform of A003960 (with alternating zeros omitted).
%H A003970 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%F A003970 Multiplicative with a(p^e) = [(p-1)/2][(p+1)/2]^(e-1). - _David W. Wilson_, Sep 01 2001
%e A003970 The Möbius transform begins 1,0,1,0,2,0,3,0,2,0,5,0,6,0,2,0,8,0,9,0,3,0,11,0,...
%t A003970 f[p_, e_] := ((p - 1)/2) ((p + 1)/2)^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[2*n - 1]; Array[a, 100] (* _Amiram Eldar_, Nov 03 2023 *)
%o A003970 (PARI) a(n) = {my(f = factor(2*n-1)); for (i=1, #f~, p = f[i, 1]; f[i, 1] = (p-1)/2*((p+1)/2)^(f[i,2]-1); f[i, 2] = 1); factorback(f);} \\ _Michel Marcus_, Feb 27 2015
%Y A003970 Cf. A003960.
%K A003970 nonn,easy,mult
%O A003970 1,3
%A A003970 _Marc LeBrun_
%E A003970 More terms from _Reiner Martin_, Aug 15 2001
%E A003970 Further terms from _David W. Wilson_, Aug 29 2001