A347960 Numbers k for which A348036(k) > A007947(k).

36, 72, 100, 108, 144, 180, 196, 200, 216, 225, 252, 288, 300, 324, 360, 392, 396, 400, 432, 450, 468, 484, 500, 504, 540, 576, 588, 600, 612, 648, 675, 676, 684, 700, 720, 756, 784, 792, 800, 828, 864, 900, 936, 968, 972, 980, 1000, 1008, 1044, 1080, 1089, 1100, 1116, 1125, 1152, 1156, 1176, 1188, 1200, 1224, 1260, 1296

Offset: 1

Author

Antti Karttunen, Oct 19 2021

Keywords

• nonn

Comments

Numbers k such that A348039(k) > 1.

Numbers k such that A348037(k) < A003557(k).

Numbers k such that A327564(k) > A348038(k).

Differs from A036785 and A338539 for the first time at n=20, where a(n) = 450, as A036785(20) = A338539(20) = 441 is not included in this sequence.

Crossrefs

Cf. A003557, A003959, A003968, A007947, A327564, A348036, A348037, A348038, A348039.

Programs

Mathematica

f[p_, e_] := p*(p + 1)^(e - 1); q[n_] := GCD[n, Times @@ f @@@ (fct = FactorInteger[n])] > Times @@ First /@ fct; Select[Range[1300], q] (* Amiram Eldar, Oct 20 2021 *)

PARI

A003968(n) = {my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); }
A007947(n) = factorback(factorint(n)[, 1]);
A348036(n) = gcd(n, A003968(n));
isA347960(n) = (A348036(n)>A007947(n));