A374785 - OEIS

A374785

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

223092870, 281291010, 300690390, 6469693230, 6915878970, 8254436190, 8720021310, 9146807670, 9592993410, 10407767370, 10485364890, 10555815270, 11125544430, 11532931410, 11797675890, 11823922110, 12095513430, 12328305990, 12598876290, 12929686770, 13162479330

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OFFSET

1,1

COMMENTS

Numbers k such that A374783(k)/A374784(k) > 2.

The least odd term is A070826(43) = 5.154... * 10^74, and the least term that is coprime to 6 is Product_{k=3..219} prime(k) = 1.0459... * 10^571.

The least nonsquarefree (A013929) term is a(613) = 148802944290 = 2 * 3 * 5 * 7 * 11 * 13 * 17 *19 * 23^2 * 29.

All the terms are nonpowerful numbers (A052485). For powerful numbers (A001694) k, A374783/(k)/A374784(k) < Product_{p prime} (1 + 1/(2*p)) = 1.242534... (A366586).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000

FORMULA

A001221(a(n)) >= 9.

EXAMPLE

223092870 is a term since A374783(223092870)/A374784(223092870) = 666225/330752 = 2.014... > 2.

MATHEMATICA

f[p_, e_] := 1 + 1/(2*p^e); r[1] = 1; r[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[4*10^8], s[#] > 2 &]

PROG

(PARI) is(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + 1/(2*f[i, 1]^f[i, 2])) > 2; }

CROSSREFS

Subsequence of A052485.