A249738 a(n) = 0 if n is 1 or a prime, otherwise, when n = A020639(n) * A032742(n), a(n) = the largest k < A032742(n) such that either k = 1 or A020639(k) >= A020639(n), where A020639(n) and A032742(n) are the smallest prime and the largest proper divisor dividing n.

0, 0, 0, 1, 0, 2, 0, 3, 1, 4, 0, 5, 0, 6, 3, 7, 0, 8, 0, 9, 5, 10, 0, 11, 1, 12, 7, 13, 0, 14, 0, 15, 9, 16, 5, 17, 0, 18, 11, 19, 0, 20, 0, 21, 13, 22, 0, 23, 1, 24, 15, 25, 0, 26, 7, 27, 17, 28, 0, 29, 0, 30, 19, 31, 11, 32, 0, 33, 21, 34, 0, 35, 0, 36, 23, 37, 7, 38, 0, 39, 25, 40, 0, 41, 13, 42, 27, 43, 0, 44, 11, 45, 29, 46, 17, 47, 0, 48, 31, 49, 0, 50

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

Other identities:

a(n) = A249744(n) / A020639(n).

a(k) = 1 if and only if k is one of A001248 (squares of primes).

Prog

(Scheme) (define (A249738 n) (cond ((or (= 1 n) (prime? n)) 0) (else (let ((lpf (A020639 n))) (let loop ((k (- (A032742 n) 1))) (cond ((= 1 k) k) ((>= (A020639 k) lpf) k) (else (loop (- k 1)))))))))

Crossrefs

Cf. A020639, A032742, A078898, A249744.

Sequence in context: A243056 A338568 A279119 * A364020 A363898 A110514

Adjacent sequences: A249735 A249736 A249737 * A249739 A249740 A249741

Keyword

nonn

Author

Antti Karttunen, Dec 06 2014

Status

approved