A371098 -id:A371098

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A324198

a(n) = gcd(n, A276086(n)), where A276086 is the primorial base exp-function.

+10
59

1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 15, 1, 1, 1, 1, 5, 3, 1, 1, 1, 25, 1, 3, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 3, 5, 1, 7, 1, 1, 15, 1, 1, 1, 7, 25, 3, 1, 1, 1, 5, 7, 3, 1, 1, 1, 1, 1, 21, 1, 1, 1, 1, 1, 3, 35, 1, 1, 1, 1, 75, 1, 7, 1, 1, 5, 3, 1, 1, 7, 5, 1, 3, 1, 1, 1, 7, 1, 3, 1, 1, 1, 1, 49, 3, 5, 1, 1, 1, 1, 105

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to primorial base

FORMULA

a(n) = gcd(n, A276086(n)).

From Antti Karttunen, Oct 21 2019: (Start)

A000005(a(n)) = A327168(n).

a(A328316(n)) = A328323(n).

a(n) = A324580(n) / A328584(n).

(End)

MATHEMATICA

Array[Block[{i, m, n = #, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; GCD[#, m]] &, 106, 0] (* Michael De Vlieger, Feb 04 2022 *)

PROG

(PARI)

A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };

A324198(n) = gcd(n, A276086(n));

(PARI) A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); }; \\ Antti Karttunen, Oct 21 2019

CROSSREFS

Cf. A003989, A276086, A323878, A324284, A324350, A324351, A324384, A324577, A324580, A324646, A327858, A328323, A327168, A328316, A328323, A328386, A328584, A346242 (Dirichlet inverse), A351254.

Cf. A324583 (positions of ones), A324584 (and terms larger than one).

Cf. A371098 (odd bisection), A371099 [= a(36n+9)].

Cf. also A328231.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 25 2019

STATUS

approved

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