A356173 a(n) = 1 if n is not divisible by two consecutive prime numbers, otherwise 0.

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

Offset

1

Comments

a(n) = 1 if n and A003961(n) are coprime, otherwise 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = [1 == gcd(n,A003961(n))], where [ ] is the Iverson bracket.

a(n) = 1 - A296210(n).

Mathematica

a[n_] := If[SequenceCount[FactorInteger[n][[;; , 1]], {p1_, p2_} /; p2 == NextPrime[p1]] == 0, 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 29 2022 *)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356173(n) = (1==gcd(n, A003961(n)));

Crossrefs

Characteristic function of A319630.

Cf. A003961, A296210, A322361, A356172.

Sequence in context: A345009 A071040 A336834 * A294934 A360128 A174340

Adjacent sequences: A356170 A356171 A356172 * A356174 A356175 A356176

Keyword

nonn

Author

Antti Karttunen, Jul 29 2022

Status

approved