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

155925, 225225, 259875, 294525, 297675, 363825, 405405, 429975, 467775, 496125, 552825, 562275, 571725, 606375, 628425, 675675, 694575, 760725, 765765, 779625, 883575, 893025, 921375, 945945, 987525, 1044225, 1091475, 1126125, 1167075, 1195425, 1216215, 1289925

Offset: 1

Author

Amiram Eldar, Sep 20 2021

Keywords

• nonn

Comments

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...

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

Examples

			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.
		

Links

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

Crossrefs

The odd terms of A347935.

Subsequence of A005101 and A005231.

Cf. A187795.

Programs

Mathematica

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

PARI

isok(k) = (k%2) && sumdiv(k, d, if (sigma(d)>=2*d, d)) > 2*k; \\ Michel Marcus, Sep 20 2021