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
Links
- Ivan Neretin, Table of n, a(n) for n = 1..10000
Programs
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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 *)
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PARI
for(n=1, 320, if((n*(n!))%(n^numdiv(n))==0, print1(n, ", ")))
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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
Comments