A374780 Odd terms in A245214.

10854718875, 12131744625, 13408770375, 18091198125, 19538493975, 20219574375, 21070924875, 22347950625, 22915517625, 23880381525, 24902002125, 25327677375, 28307404125, 28733079375, 29462808375, 32564156625, 35118208125, 36395233875, 39800635875, 40226311125

Offset: 1

Author

Amiram Eldar, Jul 19 2024

Keywords

• nonn

Comments

Odd numbers whose divisors have a mean abundancy index that is larger than 2.

The odd terms in A245214 are relatively rare: a(1) = A245214(276918705).

The least term that is not divisible by 3 is 26115176669245401228259189019322202117310546875.

Examples

			10854718875 is a term since it is odd and A374777(10854718875) / A374778(10854718875) = 11975203 / 5955950 = 2.0106... > 2.
		

Crossrefs

Subsequence of A245214.

Cf. A005231, A374777, A374778.

Programs

Mathematica

f[p_, e_] := ((e+1)*p^2 - (e+2)*p + p^(-e))/((e+1)*(p-1)^2); s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; seq[kmax_] := Module[{v = {}}, Do[If[s[k] > 2, AppendTo[v, k]], {k, 1, kmax, 2}]; v]; seq[2*10^10]

PARI

is(k) = if(!(k % 2), 0, my(f = factor(k)); prod(i = 1, #f~, p=f[i,1]; e=f[i,2]; (-2*p - e*p + p^2 + e*p^2 + p^(-e))/((e + 1)*(p - 1)^2)) > 2);