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

14, 124, 585, 1016, 16748, 32085, 33892, 37882, 39962, 41925, 46665, 121605, 134589, 181305, 212175, 388455, 495465, 522488, 524224, 544065, 839865, 1061565, 1152921, 1165515, 1243275, 1247103, 1335411, 1676829, 1943638, 2151075, 2290869, 2478075, 2625514, 2673998

Offset: 1

Author

Amiram Eldar, Mar 06 2025

Keywords

• nonn

Comments

Numbers k such that k^2 is primitive abundant number (A091191).

If p is an odd Mersenne exponent (A174265), then 2^((p-1)/2) * (2^p-1) is a term.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..775

Crossrefs

Subsequence of A381738.

A379950 is a subsequence.

Cf. A005101, A091191, A174265, A263837, A341358, A379949.

Programs

Mathematica

q[k_] := DivisorSigma[-1, k^2] > 2 &&  AllTrue[Divisors[k], DivisorSigma[-1, #*k] <= 2 || # == k &]; Select[Range[10^6], q]

PARI

isok(k) = fordiv(k, d, if(d < k && sigma(d*k, -1) > 2, return(0))); sigma(k^2, -1) > 2;