A387420 Numbers k such that sigma(k) < 2*A057521(k), where A057521(n) gives the powerful part of n, and sigma is the sum of divisors function.

1, 4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 169, 225, 243, 256, 289, 343, 361, 441, 484, 512, 529, 625, 675, 676, 729, 841, 961, 1024, 1089, 1125, 1156, 1225, 1323, 1331, 1369, 1444, 1521, 1681, 1849, 2025, 2048, 2116, 2187, 2197, 2209, 2312, 2401, 2601, 2809, 2888, 3025, 3087, 3125, 3249, 3267, 3364, 3375

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sigma(n).

Formula

{k | A000203(k)/A057521(k) < 2}.

Example

225 = 3^2 * 5^2 is present, as sigma(225) = 403 < 2*225 = 450.

Mathematica

A387420Q[k_] := DivisorSigma[1, k] < 2*Times @@ Power @@@ Select[FactorInteger[k], Last[#] > 1 &];
Select[Range[5000], A387420Q] (* Paolo Xausa, Sep 13 2025 *)

Prog

(PARI)
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); };
is_A387720(n) = (sigma(n) < 2*A057521(n));

Crossrefs

Cf. A000203, A052485, A052486, A057521, A387421 (complement).

Subsequence of A001694.

Subsequences: A025475, A379164.

Sequence in context: A134601 A227476 A319163 * A134611 A134612 A025475

Adjacent sequences: A387417 A387418 A387419 * A387421 A387422 A387423

Keyword

nonn

Author

Antti Karttunen, Sep 12 2025

Status

approved