A356172 a(n) = 1 if n is odd and not divisible by two consecutive prime numbers, otherwise 0.

1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1

Offset

1

Comments

a(n) = 1 if n is odd and relatively prime to A003961(n), otherwise 0.

a(n) = 1 if n and the smallest positive k such that n divides k*A003961(k) are coprime, otherwise 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A000035(n) * A356173(n).

a(n) = [gcd(n, A356164(n)) == 1], where [ ] is the Iverson bracket.

a(n) = [A356166(n) == 1] = [A356169(n) == 0].

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356172(n) = ((n%2)&&(1==gcd(n, A003961(n))));
(PARI)
\\ Alternatively (slow!):
A356172(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(1==gcd(n, k))));

Crossrefs

Characteristic function of A356171.

Cf. A000035, A003961, A322361, A356164, A356166, A356169, A356173.

Sequence in context: A014485 A014373 A014317 * A015813 A015901 A016077

Adjacent sequences: A356169 A356170 A356171 * A356173 A356174 A356175

Keyword

nonn

Author

Antti Karttunen, Jul 28 2022

Status

approved