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 A069149 Numbers k such that k*k!/A062758(k) is an integer where A062758(k) is the product of squares of divisors of n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 *) 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

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Last modified January 19 04:09 EST 2020. Contains 331031 sequences. (Running on oeis4.)