A381739 Number k such that k^2 is abundant, and d^2 is nonabundant for any proper divisor d of k.

6, 10, 14, 44, 52, 68, 76, 92, 105, 116, 124, 286, 296, 328, 344, 374, 376, 418, 424, 442, 472, 488, 495, 506, 536, 568, 584, 585, 632, 664, 712, 776, 808, 824, 856, 872, 904, 1016, 2096, 2145, 2192, 2224, 2384, 2416, 2512, 2608, 2672, 2768, 2805, 2864, 2896, 3056

Offset: 1

Author

Amiram Eldar, Mar 05 2025

Keywords

• nonn
• easy

Comments

The primitive terms of A381738. Each term of A381738 is a multiple of a term in this sequence.

Links

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

Crossrefs

Subsequence of A381738.

A381741 is a subsequence.

Cf. A005101, A263837.

Programs

Mathematica

q[k_] := DivisorSigma[-1, k^2] > 2 && AllTrue[Divisors[k], DivisorSigma[-1, #^2] <= 2 || # == k &]; Select[Range[3200], q]

PARI

is1(k) = {my(f = factor(k)); prod(i = 1, #f~, f[i,2] *= 2); sigma(f, -1) > 2;}
isok(k) = if(!is1(k), 0, fordiv(k, d, if(d < k && is1(d), return(0))); 1);