A373489 a(n) = 1 if A003415(n) is a multiple of A276085(n), otherwise 0, where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = [n==1 or A373147(n)==0], 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]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };
A373489(n) = (n<=2 || (!isprime(n) && !(A003415(n)%A276085(n))));
(PARI) A373489(n) = if(n<=2, !!n, if(isprime(n), 0, my(f=factor(n), ad=n*sum(i=1, #f~, f[i, 2]/f[i, 1]), pr=1, q=1, s=0); for(k=1, #f~, forprime(p = nextprime(1+q), f[k, 1]-1, pr *= p; if(pr > ad, return(0)); q = p); s += f[k, 2]*pr; if(s > ad, return(0))); !(ad%s))); \\ Antti Karttunen, Jan 29 2026

Crossrefs

Characteristic function of A373490.

Cf. A003415, A276085, A373147.

Cf. also A373486.

Sequence in context: A181101 A379274 A321512 * A297054 A359349 A266459

Adjacent sequences: A373486 A373487 A373488 * A373490 A373491 A373492

Keyword

nonn

Author

Antti Karttunen, Jun 09 2024

Status

approved