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.

A307227 Numbers k such that A060648(k) is divisible by k.

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%I A307227 #13 May 07 2019 15:16:10
%S A307227 1,2,105,210,20349,36075,40698,72150,7162155,9258795,14324310,
%T A307227 18517590,117972855,156818025,235945710,313636050,5448196215,
%U A307227 10896392430
%N A307227 Numbers k such that A060648(k) is divisible by k.
%C A307227 If k is an odd term of this sequence then 2*k is also a term.
%C A307227 The quotients A060648(a(n))/a(n) are 1, 2, 3, 6, 3, 3, 6, 6, 5, 5, 10, 10, 5, 5, 10, 10, ...
%C A307227 Also terms are: 75293843625, 89741043315, 150587687250, 179482086630, 459768040875, 919536081750, 1871844556725, 3743689113450, 30832458453225, 57275447662125, 61664916906450, 114550895324250. - _David A. Corneth_, Mar 29 2019
%t A307227 f[p_, e_] := (p^(e + 1) + p^e - 2)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; aQ[n_] := Divisible[a[n], n]; Select[Range[10^7], aQ]
%o A307227 (PARI) f(n) = sumdiv(n, d,  2^omega(d)*(n/d) ); \\ A060648
%o A307227 isok(n) = !(f(n) % n); \\ _Michel Marcus_, Mar 30 2019
%o A307227 (PARI) \\ for is(n), see isok(n) above \\ _David A. Corneth_, Mar 30 2019
%o A307227 A060648(n) = {my(f = factor(n), res = 1); for(i = 1, #f~, res *= (f[i, 1]^(f[i, 2]+1)+f[i, 1]^f[i, 2]-2)/(f[i, 1]-1)); res} \\ _David A. Corneth_, Mar 30 2019
%Y A307227 Cf. A060648.
%K A307227 nonn,more
%O A307227 1,2
%A A307227 _Amiram Eldar_, Mar 29 2019