A374788 - OEIS

%I #6 Jul 20 2024 14:41:52

%S 7560,9240,10920,83160,98280,120120,120960,128520,143640,147840,

%T 154440,157080,173880,174720,175560,185640,189000,190080,201960,

%U 207480,212520,216216,219240,224640,225720,228480,231000,234360,238680,251160,255360,266112,266760,267960

%N Numbers whose infinitary divisors have a mean infinitary abundancy index that is larger than 2.

%C Numbers k such that A374786(k)/A374787(k) > 2.

%C The least odd term is 17737266779965459404793703604641625, and the least term that is coprime to 6 is 5^7 * (7 * 11 * ... * 23)^3 * 29 * 31 * ... * 751 = 3.140513... * 10^329.

%H Amiram Eldar, <a href="/A374788/b374788.txt">Table of n, a(n) for n = 1..10000</a>

%e 7560 is a term since A374786(7560)/A374787(7560) = 1045/512 = 2.041... > 2.

%t f[p_, e_] := p^(2^(-1 + Position[Reverse@IntegerDigits[e, 2], _?(# == 1 &)])); q[1] = False; q[n_] := Times @@ (1 + 1/(2*Flatten@ (f @@@ FactorInteger[n]))) > 2; Select[Range[300000], q]

%o (PARI) is(n) = {my(f = factor(n), b); prod(i = 1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 1 + 1/(2*f[i, 1]^(2^(#b-k))), 1))) > 2;}

%Y Cf. A129656, A374786, A374787.

%Y Similar sequences: A245214, A374785.

%K nonn

%O 1,1

%A _Amiram Eldar_, Jul 20 2024