cp's OEIS Frontend

A067807 Numbers k such that sigma(k)^2 > 2*sigma(k^2).

%I A067807 #29 May 03 2025 07:45:21
%S A067807 24,36,40,48,60,72,80,84,90,96,108,112,120,126,132,140,144,156,160,
%T A067807 168,176,180,192,200,204,208,210,216,224,228,240,252,264,270,276,280,
%U A067807 288,300,312,320,324,336,348,352,360,372,378,384,392,396,400,408,416,420
%N A067807 Numbers k such that sigma(k)^2 > 2*sigma(k^2).
%C A067807 For every n>1 sigma(n)^2 > sigma(n^2).
%C A067807 Limit_{n->oo} a(n)/n appears to exist and is near 8.0; e.g., a(124094) = 1000000. - _Paul D. Hanna_, Sep 22 2011
%C A067807 We also have a(12438441) = 10^8, a(124240921) = 10^9, and a(1242729194) = 10^10. - _Giovanni Resta_, Jun 15 2018
%C A067807 All the terms are abundant numbers (A005101). - _Amiram Eldar_, May 03 2025
%H A067807 Paul D. Hanna, <a href="/A067807/b067807.txt">Table of n, a(n) for n = 1..1000</a>
%e A067807 The limit a(n)/n seems to be near 8.0:
%e A067807         n     a(n)    a(n)/n
%e A067807   ------- --------  ----------
%e A067807    124094  1000000  8.05840...
%e A067807    248310  2000000  8.05444...
%e A067807    372503  3000000  8.05362...
%e A067807    496826  4000000  8.05110...
%e A067807    621163  5000000  8.04941...
%e A067807    745602  6000000  8.04718...
%e A067807    870189  7000000  8.04422...
%e A067807    994799  8000000  8.04182...
%e A067807   1119336  9000000  8.04048...
%e A067807   1243884 10000000  8.03933...
%t A067807 Select[Range[500],DivisorSigma[1,#]^2>2DivisorSigma[1,#^2]&]  (* _Harvey P. Dale_, Mar 30 2011 *)
%o A067807 (PARI) {for(n=1,8000,if(2*sigma(n^2)-sigma(n)^2 < 0,print1(n,",")))} \\ _Paul D. Hanna_, Sep 22 2011
%Y A067807 Cf. A000203 (sigma), A195735, A065764.
%Y A067807 Subsequence of A005101.
%K A067807 nonn
%O A067807 1,1
%A A067807 _Benoit Cloitre_, Feb 07 2002