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

Author

Antti Karttunen, Dec 06 2014

Keywords

• nonn

Links

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

Crossrefs

Cf. A020639, A032742, A078898, A249744.

Programs

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)))))))))

Formula

Other identities:

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

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