A381741 Squarefree numbers k such that k^2 is abundant, and d^2 is nonabundant for any proper divisor d of k.

6, 10, 14, 105, 286, 374, 418, 442, 506, 2145, 2805, 3135, 3315, 3705, 3795, 4485, 4785, 4845, 5115, 5655, 6045, 6105, 6765, 7095, 7755, 8745, 9735, 10065, 11362, 14326, 14858, 15314, 17342, 18278, 18538, 18734, 19778, 20026, 20254, 21242, 22126, 22678, 23218

Offset: 1

Author

Amiram Eldar, Mar 06 2025

Keywords

• nonn
• easy

Comments

The primitive terms of A381740. Each term of A381740 is a multiple of a term in this sequence.

Links

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

Crossrefs

Intersection of A005117 and A381739.

Subsequence of A381738 and A381740.

Cf. A005101, A263837.

Programs

Mathematica

q[k_] := SquareFreeQ[k] && DivisorSigma[-1, k^2] > 2 && AllTrue[Divisors[k], DivisorSigma[-1, #^2] <= 2 || # == k &]; Select[Range[24000], q]

PARI

is1(k) = {my(f = factor(k)); if(!issquarefree(f), 0, 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);