A322445 Smallest positive integer m such that n divides A297707(m).

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

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: A088492 A345931 A025492 * A276035 A077004 A064760

Adjacent sequences: A322442 A322443 A322444 * A322446 A322447 A322448

Keyword

nonn

Author

Lechoslaw Ratajczak, Dec 08 2018

Status

approved