A374788 -id:A374788 - cp's OEIS frontend

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

Offset: 1

Amiram Eldar, Jul 20 2024

nonn

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).

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

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

Subsequence of A052485.
Cf. A001221, A001694, A013929, A034683, A070826, A366586, A374783, A374784.
Similar sequences: A245214, A374788.

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

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

A001221(a(n)) >= 9.

cp's OEIS Frontend

A374785 Numbers whose unitary divisors have a mean unitary abundancy index that is larger than 2.

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