login
A374788
Numbers whose infinitary divisors have a mean infinitary abundancy index that is larger than 2.
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
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
Similar sequences: A245214, A374785.
Sequence in context: A234987 A157322 A172443 * A190108 A308913 A145313
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 20 2024
STATUS
approved