A067847 - OEIS

%I #13 Apr 19 2019 12:10:58

%S 1,2,3,5,9,15,27,40,63,100,180,248,459,696,1019,1299,2495,3219,6011,

%T 7986,11247,17029,32567,39501,53017,79775,97251,126981,245675,301054,

%U 582853,668274,921616,1382954,1811949,2097059,4088346,6142187,8417004

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

%H Ray Chandler, <a href="/A067847/b067847.txt">Table of n, a(n) for n=1..42</a>

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

%e 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

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

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

%Y Cf. A067513, A156190.

%K nonn

%O 1,2

%A _Vladeta Jovovic_, Feb 14 2002

%E More terms from _Sascha Kurz_, Mar 19 2002

%E More terms from _Naohiro Nomoto_, Mar 13 2002

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

%E a(28)=118584 from _Vladeta Jovovic_, Apr 07 2004

%E Corrected a(28)=126981 and added a(29)-a(31) by _Ray Chandler_, Feb 03 2009

%E a(32)-a(42) from _Ray Chandler_, Feb 05 2009