A364491 - OEIS

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A364491

a(n) = n / gcd(n, A163511(n)).

0, 1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 15, 1, 17, 1, 19, 5, 7, 11, 23, 1, 5, 13, 27, 7, 29, 15, 31, 1, 11, 17, 7, 1, 37, 19, 39, 5, 41, 7, 43, 11, 15, 23, 47, 1, 49, 5, 51, 13, 53, 27, 5, 7, 19, 29, 59, 15, 61, 31, 63, 1, 65, 11, 67, 17, 23, 7, 71, 1, 73, 37, 15, 19, 11, 39, 79, 5, 3, 41, 83, 7, 17, 43, 87

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

OFFSET

0,6

COMMENTS

Numerator of n / A163511(n).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16383

FORMULA

a(n) = n / A364255(n) = n / gcd(n, A163511(n)).

PROG

(PARI)

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429

A163511(n) = if(!n, 1, A005940(1+A054429(n)))

A364491(n) = (n/gcd(n, A163511(n)));

(Python)

from math import gcd

from sympy import nextprime

def A364491(n):

c, p, k = 1, 1, n

while k:

c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())

k >>= s+1

return n//gcd(c*p, n) # Chai Wah Wu, Jul 26 2023

CROSSREFS

Cf. A163511, A364255, A364492 (denominators), A364493, A364494 (positions of 1's).

Sequence in context: A065330 A140215 A366284 * A190643 A068328 A342918

Adjacent sequences: A364488 A364489 A364490 * A364492 A364493 A364494

KEYWORD

nonn,frac

AUTHOR

Antti Karttunen, Jul 26 2023

STATUS

approved