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

1,1

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.

Links

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

Example

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

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]

Prog

(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; }

Crossrefs

Cf. A129656, A374786, A374787.

Similar sequences: A245214, A374785.

Sequence in context: A234987 A157322 A172443 * A190108 A308913 A145313

Adjacent sequences: A374785 A374786 A374787 * A374789 A374790 A374791

Keyword

nonn

Author

Amiram Eldar, Jul 20 2024

Status

approved