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A322445 Smallest positive integer m such that n divides A297707(m). 0
1, 2, 3, 4, 5, 3, 7, 4, 3, 5, 11, 4, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 4, 5, 13, 6, 7, 29, 5, 31, 4, 11, 17, 7, 5, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 4, 7, 5, 17, 13, 53, 6, 11, 7, 19, 29, 59, 5, 61, 31, 7, 4, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If p is prime, a(p) = p.

The first three integers n for which a(n!) is not a prime number are: 1 (a(1!) = 1), 4 (a(4!) = 4), 10 (a(10!) = 8). Is there a larger n? If such a number n exists, it is greater than 2000.

The smallest integer n satisfying the equation a(n) = a(n+1) is 2400 (a(2400) = a(2401) = 7). Is there a larger n? If such a number n exists, it is greater than 3000.

LINKS

Table of n, a(n) for n=1..65.

J. Sondow and E. W. Weisstein, MathWorld: Smarandache Function

EXAMPLE

a(12) = 4 because 12 is not divisible by A297707(1) = 1, A297707(2) = 2*1, A297707(3) = 3*2*1*3*1, and is divisible by A297707(4) = 4*3*2*1*4*2*4*1.

MATHEMATICA

f[n_] := n^(n - 1) *  Product[k^DivisorSigma[0, n - k], {k, n - 1}]; a[n_] := Module[{k = 1}, While[! Divisible[f[k], n], k++]; k]; Array[a, 60] (* Amiram Eldar, Dec 08 2018 *)

PROG

(PARI) f(n) = (n^(n-1))*prod(k=1, n-1, k^numdiv(n-k)); \\ A297707

a(n) = {my(k=1); while (f(k) % n, k++); k; } \\ Michel Marcus, Dec 09 2018

CROSSREFS

Cf. A002034, A007922, A063917.

Sequence in context: A330750 A088492 A025492 * A276035 A077004 A064760

Adjacent sequences:  A322442 A322443 A322444 * A322446 A322447 A322448

KEYWORD

nonn

AUTHOR

Lechoslaw Ratajczak, Dec 08 2018

STATUS

approved

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Last modified May 11 03:49 EDT 2021. Contains 343784 sequences. (Running on oeis4.)