A067847 Number of divisors d of n! such that d+1 is prime.

1, 2, 3, 5, 9, 15, 27, 40, 63, 100, 180, 248, 459, 696, 1019, 1299, 2495, 3219, 6011, 7986, 11247, 17029, 32567, 39501, 53017, 79775, 97251, 126981, 245675, 301054, 582853, 668274, 921616, 1382954, 1811949, 2097059, 4088346, 6142187, 8417004

Offset

1,2

Links

Ray Chandler, Table of n, a(n) for n=1..42

Formula

a(n) = A067513(A000142(n)).

Example

a(5)=9 because the divisors of 5!=120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 60 and 120 and the primes are 2, 3, 5, 7, 11, 13, 31, 41 and 61

Mathematica

Table[Count[Divisors[n!]+1, _?PrimeQ], {n, 40}] (* Harvey P. Dale, Apr 19 2019 *)

Prog

(PARI) a(n)=s=0; fordiv (n!, i, if(isprime(n!/i+1), s=s+1)); return(s);

Crossrefs

Cf. A067513, A156190.

Sequence in context: A129852 A367666 A065954 * A190138 A273905 A307074

Adjacent sequences: A067844 A067845 A067846 * A067848 A067849 A067850

Keyword

nonn

Author

Vladeta Jovovic, Feb 14 2002

Extensions

More terms from Sascha Kurz, Mar 19 2002

More terms from Naohiro Nomoto, Mar 13 2002

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 26 2004

a(28)=118584 from Vladeta Jovovic, Apr 07 2004

Corrected a(28)=126981 and added a(29)-a(31) by Ray Chandler, Feb 03 2009

a(32)-a(42) from Ray Chandler, Feb 05 2009

Status

approved