A392603 Numbers k such that A380459(A276086(k)) has no divisors of the form p^p, for any prime p.

0, 1, 2, 3, 6, 30, 31, 210, 2310, 2311, 30030, 510510, 510511, 9699690, 223092870, 6469693230, 6469693231, 6469693233, 6469693261, 200560490130, 200560490131, 7420738134810, 304250263527210, 304250263527211, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070, 1922760350154212639071

Offset

1,3

Comments

Sequence A276085(A380468(.)) sorted into ascending order.

Numbers k such that A276086(k) is in A380468.

It is conjectured that A267263(a(n)), and equally, A276150(a(n)), is always <= 4. See A380475.

Links

Antti Karttunen, Table of n, a(n) for n = 1..52

Index entries for sequences related to primorial base.

Formula

{k such that A380467(A276086(k)) = 1}.

a(n) = A276156(A392604(n)).

Prog

(PARI)
A359550(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(0)); if(pp > n, return(1))); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A349394(n) = { my(p=0, e); if((e=isprimepower(n, &p)), p^(e-1), 0); };
A380459(n) = { my(m=1); fordiv(n, d, m *= A276086(d)^A349394(n/d)); (m); };
A380467(n) = A359550(A380459(n));
A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };
is_A392603(n) = (A328114(n)<2 && A380467(A276086(n)));

Crossrefs

Cf. A002110 (subsequence), A267263, A276085, A276086, A276150, A327860, A380459, A380467, A380468, A380475, A380476, A392604.

Subsequence of A276156.

Sequence in context: A277809 A051717 A330030 * A192441 A108326 A002234

Adjacent sequences: A392600 A392601 A392602 * A392604 A392605 A392606

Keyword

nonn,base

Author

Antti Karttunen, Jan 21 2026

Status

approved