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A347936 Odd numbers k such that A187795(k) > 2*k. 3

%I #11 Sep 20 2021 18:29:39

%S 155925,225225,259875,294525,297675,363825,405405,429975,467775,

%T 496125,552825,562275,571725,606375,628425,675675,694575,760725,

%U 765765,779625,883575,893025,921375,945945,987525,1044225,1091475,1126125,1167075,1195425,1216215,1289925

%N Odd numbers k such that A187795(k) > 2*k.

%C The numbers of terms not exceeding 10^k for k = 6, 7, ... are 25, 352, 3281, 33291, 336686, ... Apparently, this sequence has an asymptotic density 0.000033...

%C Apparently, the least term that is not divisible by 3 is 836504377583875.

%H Amiram Eldar, <a href="/A347936/b347936.txt">Table of n, a(n) for n = 1..10000</a>

%e The divisors of 155925 that are abundant numbers are {945, 1575, 2835, 3465, 4725, 5775, 7425, 10395, 14175, 17325, 22275, 31185, 51975, 155925}. Their sum is 330000 > 2*155925 = 311850. Therefore, 155925 is a term.

%t abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; Select[Range[1, 1000000, 2], q]

%o (PARI) isok(k) = (k%2) && sumdiv(k, d, if (sigma(d)>=2*d, d)) > 2*k; \\ _Michel Marcus_, Sep 20 2021

%Y The odd terms of A347935.

%Y Subsequence of A005101 and A005231.

%Y Cf. A187795.

%K nonn

%O 1,1

%A _Amiram Eldar_, Sep 20 2021

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Last modified May 24 05:24 EDT 2024. Contains 372772 sequences. (Running on oeis4.)