A374788 Numbers whose infinitary divisors have a mean infinitary abundancy index that is larger than 2.

7560, 9240, 10920, 83160, 98280, 120120, 120960, 128520, 143640, 147840, 154440, 157080, 173880, 174720, 175560, 185640, 189000, 190080, 201960, 207480, 212520, 216216, 219240, 224640, 225720, 228480, 231000, 234360, 238680, 251160, 255360, 266112, 266760, 267960

Offset: 1

Author

Amiram Eldar, Jul 20 2024

Keywords

• nonn

Comments

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

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.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A129656, A374786, A374787.

Similar sequences: A245214, A374785.

Programs

Mathematica

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]

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;}