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A374779
Numbers whose divisors have a mean abundancy index that is larger than 3.
2
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
1,1
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.
LINKS
EXAMPLE
10886400 is a term since A374777(10886400)/A374778(10886400) = 70644571/23514624 = 3.004... > 3.
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 &]
PROG
(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; }
CROSSREFS
Subsequence of A245214.
Sequence in context: A205664 A205953 A205464 * A202470 A224639 A298704
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 19 2024
STATUS
approved