A369961 a(n) = 1 if gcd(n, A003415(n)) is equal to gcd(n, A276086(n)), otherwise 0, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

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

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Index entries for sequences related to primorial base

Formula

a(n) = [A085731(n) == A324198(n)], where [ ] is the Iverson bracket.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A369961(n) = (gcd(n, A003415(n))==gcd(n, A276086(n)));
(PARI)
A085731(n) = { my(f=factor(n)); for(i=1, #f~, if (f[i, 2] % f[i, 1], f[i, 2]--); ); factorback(f); };
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); };
A369961(n) = ((n>0) && (A085731(n)==A324198(n)));

Crossrefs

Characteristic function of A369962.

Cf. A003415, A083345, A085731, A276086, A324198, A351251.

Sequence in context: A188076 A189011 A189135 * A219189 A029691 A209229

Adjacent sequences: A369958 A369959 A369960 * A369962 A369963 A369964

Keyword

nonn

Author

Antti Karttunen, Feb 07 2024

Status

approved