The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A369937 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A369937

Numbers whose maximal exponent in their prime factorization is square.
(history; published version)

#7 by OEIS Server at Tue Feb 06 08:14:31 EST 2024

LINKS

Amiram Eldar, <a href="/A369937/b369937_1.txt">Table of n, a(n) for n = 1..10000</a>

#6 by Michael De Vlieger at Tue Feb 06 08:14:31 EST 2024

STATUS

reviewed

approved

Discussion

Tue Feb 06

08:14

OEIS Server: Installed first b-file as b369937.txt.

#5 by Joerg Arndt at Tue Feb 06 00:57:47 EST 2024

STATUS

proposed

reviewed

#4 by Amiram Eldar at Tue Feb 06 00:54:09 EST 2024

STATUS

editing

proposed

#3 by Amiram Eldar at Tue Feb 06 00:40:53 EST 2024

LINKS

Amiram Eldar, <a href="/A369937/b369937_1.txt">Table of n, a(n) for n = 1..10000</a>

#2 by Amiram Eldar at Tue Feb 06 00:39:51 EST 2024

NAME

allocated for Amiram EldarNumbers whose maximal exponent in their prime factorization is square.

DATA

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 48, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102

OFFSET

1,2

COMMENTS

First differs from A366762 at n = 84, and from A197680, A361177 and A369210 at n = 95.

Numbers k such that A051903(k) is square.

The asymptotic density of this sequence is 1/zeta(2) + Sum_{k>=2} (1/zeta(k^2+1) - 1/zeta(k^2)) = 0.64939447949574562687... .

MATHEMATICA

Select[Range[100], IntegerQ@ Sqrt[Max[FactorInteger[#][[;; , 2]]]] &]

PROG

(PARI) lista(kmax) = for(k = 1, kmax, if(k == 1 || issquare(vecmax(factor(k)[, 2])), print1(k, ", ")));

CROSSREFS

Cf. A000290, A013661, A051903.

Subsequences: A002416, A005117, A030514, A030635, A113849, A178739, A179665, A179692, A197680.

Similar sequences: A368714, A369938, A369939.

Cf. A361177, A366762, A369210.

KEYWORD

allocated

nonn,easy

AUTHOR

Amiram Eldar, Feb 06 2024

STATUS

approved

editing

#1 by Amiram Eldar at Tue Feb 06 00:15:01 EST 2024

NAME

allocated for Amiram Eldar

KEYWORD

allocated

STATUS

approved