A231715 For n with a unique factorial base representation n = du*u! + ... + d2*2! + d1*1! (each di in range 0..i, cf. A007623), a(n) = Product_{i=1..u} (gcd(d_i,i+1) mod i+1), where u is given by A084558(n).

1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2

Offset: 1

Author

Antti Karttunen, Nov 12 2013

Keywords

• nonn

Examples

			For n=13, with factorial base representation '201' (= A007623(13), 2*3! + 0*2! + 1*1! = 13) we have, starting from the least significant digit, (gcd(1,2) mod 2)*(gcd(0,3) mod 3)*(gcd(2,4) mod 4) = (1 mod 2)*(3 mod 3)*(2 mod 4) = 1*0*2 = 0, thus a(13)=0.
For n=17, with factorial base representation '221' (= A007623(17), 2*3! + 2*2! + 1*1! = 17) we have, starting from the least significant digit, (gcd(1,2) mod 2)*(gcd(2,3) mod 3)*(gcd(2,4) mod 4) = (1 mod 2)*(1 mod 3)*(2 mod 4) = 1*1*2 = 2, thus a(17)=2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080

Crossrefs

Cf. A231716 (positions of ones), A227157 (the positions of nonzero terms), A007623.

Each a(n) <= A208575(n).

Programs

Scheme

(define (A231715 n) (let loop ((n n) (i 2) (p 1)) (cond ((zero? n) p) (else (loop (floor->exact (/ n i)) (+ i 1) (* p (modulo (gcd (modulo n i) i) i)))))))