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A356172
a(n) = 1 if n is odd and not divisible by two consecutive prime numbers, otherwise 0.
5
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.
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.
Sequence in context: A014485 A014373 A014317 * A015813 A015901 A016077
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 28 2022
STATUS
approved