A069149 Numbers k such that k*k!/A062758(k) is an integer where A062758(k) is the product of squares of divisors of k.

1, 2, 3, 5, 7, 9, 11, 12, 13, 15, 17, 19, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 69, 70, 71, 72, 73, 75, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 90, 91, 93, 95, 96, 97, 98, 99

Offset

1,2

Comments

Also numbers k such that k! is divisible by k ^ (tau(k) - 1). - David A. Corneth, Apr 23 2018

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[100], Divisible[#!*#, Times @@ Divisors[#]^2] &] (* Ivan Neretin, Apr 22 2018 *)
Select[Range[100], Divisible[#!, #^(DivisorSigma[0, #] - 1)] &] (* Amiram Eldar, Jul 07 2022 *)

Prog

(PARI) for(n=1, 320, if((n*(n!))%(n^numdiv(n))==0, print1(n, ", ")))
(PARI) is(n) = {my(f = factor(n), qdiv = numdiv(f)); for(i = 1, #f~, cn = n; t = 0; while(cn \= f[i, 1], t += cn); if(t < f[i, 2] * (qdiv - 1), return(0))); 1} \\ David A. Corneth, Apr 27 2018

Crossrefs

Complement of A069148.

Cf. A001563 (n*n!), A062758.

Sequence in context: A036049 A092875 A155498 * A042996 A073040 A087268

Adjacent sequences: A069146 A069147 A069148 * A069150 A069151 A069152

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 08 2002

Status

approved