A346089 a(n) = n divided by the smallest divisor d of n for which A002034(d) = A002034(n), where A002034(n) is the smallest positive integer k such that k! is a multiple of n.

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 6, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 5, 2, 1, 3, 1, 2, 3, 4, 1, 2, 5, 8, 3, 2, 1, 12, 1, 2, 9, 2, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 5, 3, 2, 1, 12, 5, 2, 3, 8, 1, 10, 7, 4, 3, 2, 5, 3, 1, 2, 9, 4, 1, 6, 1, 8, 15

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = n / A346088(n).

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.
A346089(n) = { my(x=A002034(n)); fordiv(n, d, if(A002034(d)==x, return(n/d))); };

Crossrefs

Cf. A002034, A345935, A345936, A345944 (positions of 1's), A346088.

Cf. also A344759.

Differs from A302776 for the first time at n=27, where a(27) = 1, while A302776(27) = 3.

Sequence in context: A033103 A245661 A302789 * A302776 A366510 A366522

Adjacent sequences: A346086 A346087 A346088 * A346090 A346091 A346092

Keyword

nonn

Author

Antti Karttunen, Jul 05 2021

Status

approved