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A345931
a(n) = gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.
3
1, 2, 3, 4, 5, 3, 7, 4, 3, 5, 11, 4, 13, 7, 5, 2, 17, 6, 19, 5, 7, 11, 23, 4, 5, 13, 9, 7, 29, 5, 31, 8, 11, 17, 7, 6, 37, 19, 13, 5, 41, 7, 43, 11, 3, 23, 47, 6, 7, 10, 17, 13, 53, 9, 11, 7, 19, 29, 59, 5, 61, 31, 7, 8, 13, 11, 67, 17, 23, 7, 71, 6, 73, 37, 5, 19, 11, 13, 79, 2, 9, 41, 83, 7, 17, 43, 29, 11, 89
OFFSET
1,2
FORMULA
a(n) = gcd(n, A002034(n)) = gcd(n, A072480(n)) = gcd(A002034(n), A072480(n)).
a(n) = A002034(n) / A345932(n).
a(n) = n / A345933(n).
MATHEMATICA
Table[GCD[n, m=1; While[Mod[m!, n]!=0, m++]; m], {n, 100}] (* Giorgos Kalogeropoulos, Jul 02 2021 *)
PROG
(PARI)
A002034(n) = if(1==n, n, my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
A345931(n) = gcd(n, A002034(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 01 2021
STATUS
approved