A110417 For each k from 0 through n-1, take the largest value of C(n,r) that divides k! and sum k! / C(n,r) for all cases where C(n,r)>1.

0, 0, 0, 1, 0, 11, 0, 180, 380, 1627, 0, 379692, 0, 39168360, 19495784, 109797856, 0, 1247559689920, 0, 339677685789414, 39530054317464, 80449141757760, 0, 49078434999009645846, 4049791363412815104, 2006460609738963840

Offset

1,6

Comments

a(p) = 0, iff p is a prime. This is a generalization of sequence A110416.

Links

Table of n, a(n) for n=1..26.

Example

a(6) = 3!/(C(6,1)) + 4!/(C(6,1)) + 5!/(C(6,3)) = 1 + 4 + 6 = 11.

Prog

;; PLT DrScheme. (Zucker)
;; (! n), (binom n r) have the obvious definitions
;; (min-list a-list) produces 0 if the list is empty.
(define (A110417 n)
(local ((define (smallest-C-n-r-quotient kfactorial)
(min-list (filter integer?
(build-list (quotient n 2)
(lambda (r) (/ kfactorial (binom n (add1 r)))))))))
(apply + (build-list n (lambda (k) (smallest-C-n-r-quotient (! k)))))))

Crossrefs

Cf. A110416.

Sequence in context: A335646 A261173 A287468 * A240560 A082258 A075361

Adjacent sequences: A110414 A110415 A110416 * A110418 A110419 A110420

Keyword

easy,nonn

Author

Amarnath Murthy, Aug 01 2005

Extensions

Corrected and extended by Joshua Zucker, May 10 2006

Status

approved