A391428 Exponential abundant numbers that are squares of squarefree numbers.

900, 1764, 4356, 4900, 6084, 10404, 12996, 19044, 30276, 34596, 44100, 49284, 60516, 66564, 79524, 101124, 108900, 125316, 133956, 152100, 161604, 181476, 191844, 213444, 224676, 248004, 260100, 285156, 298116, 324900, 338724, 367236, 381924, 412164, 427716, 459684

Offset

1,1

Comments

If s is a squarefree number, then s^2 is a term if Product_{p | s} (1 + 1/p) > 2.

The primitive terms of A391427: if k is a term, then k*m is a term in A391427 for any squarefree number m that is coprime to k.

Any term in A391427 is of the form k*m where k is a term in this sequence and m is a squarefree number coprime to k. Therefore, A391427 can be generated from this sequence by multiplying with coprime squarefree numbers, and the asymptotic density of A391427 can be evaluated from the terms in this sequence (see the Comments section of A391427).

Links

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

Formula

a(n) = A087248(n)^2.

Mathematica

Select[Range[700], SquareFreeQ[#] && DivisorSigma[-1, #] > 2 &]^2

Prog

(PARI) isok(k) = {my(r); if(!issquare(k, &r), 0, my(f = factor(r)); issquarefree(f) && sigma(f, -1) > 2); }

Crossrefs

Intersection of A062503 and A129575.

Intersection of A001694 (or A000290) and A391427.

A391430 is a subsequence.

Cf. A087248, A390558.

Sequence in context: A392741 A391320 A162143 * A258888 A287800 A246887

Adjacent sequences: A391425 A391426 A391427 * A391429 A391430 A391431

Keyword

nonn,easy

Author

Amiram Eldar, Dec 09 2025

Status

approved