A100013 Number of prime factors in n!+7 (counted with multiplicity).

3, 3, 2, 1, 1, 1, 1, 3, 3, 3, 3, 2, 3, 3, 4, 2, 2, 3, 3, 5, 5, 5, 3, 4, 3, 2, 4, 5, 5, 4, 7, 6, 4, 4, 7, 2, 5, 4, 7, 4, 5, 3, 4, 6, 5, 4, 3, 3, 5, 6, 3, 5, 6, 3, 3, 7, 4, 5, 5, 2, 4, 4, 5, 4, 2, 4, 3, 5, 2, 5, 7, 4, 7, 5, 5, 3, 5, 4, 6, 6, 8, 5

Offset

0,1

References

C. Caldwell and H. Dubner, "Primorial, factorial and multifactorial primes," Math. Spectrum, 26:1 (1993/4) 1-7.

Links

Table of n, a(n) for n=0..81.

Chris Caldwell, multifactorial prime (another Prime Pages' Glossary entries).

Ken Davis, Status of Search for Multifactorial Primes.

Sean A. Irvine, Factorizations of n!+7

Example

Example 1!+7 = 2^3 so a(1) = 3.
a(3) = a(4) = a(5) = a(6) = 1 because 3!+1 = 13, 4!+7 = 31, 5!+1 = 127, 6!+7 = 727 and these are all primes. a(11) = a(15) = a(16) = a(25) = a(35) = a(59) = 2 because 11!+7 = 39916807 = 7 * 5702401, 15!+7 = 1307674368007 = 7 * 186810624001, 16!+7 = 20922789888007 = 7 * 2988969984001, 25!+7 = 15511210043330985984000007 = 7 * 2215887149047283712000001, 35!+7 = 10333147966386144929666651337523200000007 = 7 *
1476163995198020704238093048217600000001 and 59!+7 = 138683118545689835737939019720389406345902876772687432540821294940160000000000007 = 7 * 19811874077955690819705574245769915192271839538955347505831613562880000000000001 are all semiprimes.

Crossrefs

Cf. A002981, A037083, A037083, A085150, A085148, A085146, A062701, A055487, A062702.

Sequence in context: A254411 A056223 A261143 * A065744 A016455 A278702

Adjacent sequences: A100010 A100011 A100012 * A100014 A100015 A100016

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 18 2004

Extensions

More terms from Sean A. Irvine, Sep 20 2012

Status

approved