cp's OEIS Frontend

A381742 Numbers k such that k^2 is abundant but d*k is nonabundant for any proper divisor d of k.

%I A381742 #9 Mar 06 2025 01:44:06
%S A381742 14,124,585,1016,16748,32085,33892,37882,39962,41925,46665,121605,
%T A381742 134589,181305,212175,388455,495465,522488,524224,544065,839865,
%U A381742 1061565,1152921,1165515,1243275,1247103,1335411,1676829,1943638,2151075,2290869,2478075,2625514,2673998
%N A381742 Numbers k such that k^2 is abundant but d*k is nonabundant for any proper divisor d of k.
%C A381742 Numbers k such that k^2 is primitive abundant number (A091191).
%C A381742 If p is an odd Mersenne exponent (A174265), then 2^((p-1)/2) * (2^p-1) is a term.
%H A381742 Amiram Eldar, <a href="/A381742/b381742.txt">Table of n, a(n) for n = 1..775</a>
%t A381742 q[k_] := DivisorSigma[-1, k^2] > 2 &&  AllTrue[Divisors[k], DivisorSigma[-1, #*k] <= 2 || # == k &]; Select[Range[10^6], q]
%o A381742 (PARI) isok(k) = fordiv(k, d, if(d < k && sigma(d*k, -1) > 2, return(0))); sigma(k^2, -1) > 2;
%Y A381742 Subsequence of A381738.
%Y A381742 A379950 is a subsequence.
%Y A381742 Cf. A005101, A091191, A174265, A263837, A341358, A379949.
%K A381742 nonn
%O A381742 1,1
%A A381742 _Amiram Eldar_, Mar 06 2025