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.

A003969 Inverse Möbius transform of A003959.

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%I A003969 #19 Oct 23 2022 02:54:14
%S A003969 1,4,5,13,7,20,9,40,21,28,13,65,15,36,35,121,19,84,21,91,45,52,25,200,
%T A003969 43,60,85,117,31,140,33,364,65,76,63,273,39,84,75,280,43,180,45,169,
%U A003969 147,100,49,605,73,172,95,195,55,340,91,360,105,124,61,455,63,132,189
%N A003969 Inverse Möbius transform of A003959.
%H A003969 Amiram Eldar, <a href="/A003969/b003969.txt">Table of n, a(n) for n = 1..10000</a>
%F A003969 Multiplicative with a(p^e) = ((p+1)^(e+1)-1)/p. - _David W. Wilson_, Sep 01 2001
%F A003969 Sum_{k=1..n} a(k) ~ c * n^2, where c = A072691/A005596 = 2.199369... . - _Amiram Eldar_, Oct 23 2022
%t A003969 f[p_, e_] := ((p + 1)^(e + 1) - 1)/p; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 23 2022 *)
%o A003969 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, ((f[i,1] + 1)^(f[i,2] + 1) - 1)/f[i,1]); } \\ _Amiram Eldar_, Oct 23 2022
%Y A003969 Cf. A003959, A005596, A072691.
%K A003969 nonn,mult
%O A003969 1,2
%A A003969 _Marc LeBrun_
%E A003969 More terms from _David W. Wilson_, Aug 29 2001