A374779 Numbers whose divisors have a mean abundancy index that is larger than 3.

10886400, 13305600, 14515200, 18144000, 19958400, 21772800, 23587200, 23950080, 24192000, 25401600, 26611200, 27216000, 29030400, 29937600, 30481920, 31449600, 31933440, 32659200, 33264000, 33868800, 35380800, 35925120, 36288000, 37739520, 38102400, 39312000, 39916800

Offset: 1

Author

Amiram Eldar, Jul 19 2024

Keywords

• nonn

Comments

Numbers k such that A374777(k)/A374778(k) > 3.

The numbers whose mean abundancy index of divisors is larger than 2 are in A245214.

The least odd term in this sequence is 84712751711029943302437712454902728115050897458369518458984375.

Examples

			10886400 is a term since A374777(10886400)/A374778(10886400) = 70644571/23514624 = 3.004... > 3.
		

Links

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

Crossrefs

Subsequence of A245214.

Cf. A068403, 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]; Select[Range[4*10^7], s[#] > 3 &]

PARI

is(n) = {my(f = factor(n)); 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)) > 3;}