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 A275732 One-based positions of 1-digits in the factorial base representation of n are converted to primes with those indices, then multiplied together. 9
 1, 2, 3, 6, 1, 2, 5, 10, 15, 30, 5, 10, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, 2, 7, 14, 21, 42, 7, 14, 35, 70, 105, 210, 35, 70, 7, 14, 21, 42, 7, 14, 7, 14, 21, 42, 7, 14, 1, 2, 3, 6, 1, 2, 5, 10, 15, 30, 5, 10, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, 2, 5, 10, 15, 30, 5, 10, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 3, 6, 1, 2, 5, 10, 15, 30 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS All terms are squarefree (A005117), and each squarefree number occurs an infinitely many times. LINKS Antti Karttunen, Table of n, a(n) for n = 0..40320 FORMULA If A257261(n) = 0, then a(n) = 1, otherwise a(n) = A000040(A257261(n)) * a(A275730(n, A257261(n)-1)). [Here A275730(n,p) is a bivariate function that "clears" the digit at zero-based position p in the factorial base representation of n]. Other identities and observations. For all n >= 0: a(A007489(n)) = A002110(n). a(A255411(n)) = 1. A001221(a(n)) = A001222(a(n)) = A257511(n). A048675(a(n)) = A275736(n). EXAMPLE 22 has factorial base representation "320" (= A007623(22)), which does not contain any "1". Thus a(22) = 1, as the empty product is 1. 35 has factorial base representation "1121" (= A007623(35)). 1's occur in the following positions, when counted from right, starting with 1: 1, 3 and 4. Thus a(35) = prime(1)*prime(3)*prime(4) = 2*5*7 = 70. MATHEMATICA nn = 105; m = 1; While[Factorial@ m < nn, m++]; m; Map[Times @@ Map[Prime, Flatten@ Position[#, 1]] &@ Reverse@ IntegerDigits[#, MixedRadix[Reverse@ Range[2, m]]] &, Range[0, nn]] (* Michael De Vlieger, Aug 11 2016, Version 10.2 *) PROG (Scheme) ;; Recursive definition using memoizing definec-macro: (definec (A275732 n) (cond ((zero? (A257261 n)) 1) (else (* (A000040 (A257261 n)) (A275732 (A275730bi n (- (A257261 n) 1))))))) (define (A275732 n) (let loop ((z 1) (n n)) (let ((y (A257261 n))) (cond ((zero? y) z) (else (loop (* z (A000040 y)) (A275730bi n (- y 1)))))))) ;; Code for A275730bi given in A275730. (Python) from operator import mul from sympy import prime def a007623(n, p=2): return n if n

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Last modified July 12 23:28 EDT 2020. Contains 335669 sequences. (Running on oeis4.)