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
Keywords
Examples
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
Links
- Ray Chandler, Table of n, a(n) for n=1..42
Programs
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Mathematica
Table[Count[Divisors[n!]+1,?PrimeQ],{n,40}] (* _Harvey P. Dale, Apr 19 2019 *)
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PARI
a(n)=s=0;fordiv (n!,i,if(isprime(n!/i+1),s=s+1));return(s);
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