A380528 Smallest prime p such that p^p is a divisor of A380459(n), or 1 if no such factor exists, where A380459(n) = Product_{d|n} A276086(n/d)^A349394(d).

1, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 1, 3, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 1, 3, 1, 2, 2, 3, 2, 2, 1, 1, 2, 2, 1, 5, 1, 2, 2, 3, 1, 2, 2, 3, 2, 2, 1, 3, 2, 2, 2, 3, 1, 2, 1, 1, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 2, 5, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 1, 3, 2, 2, 2, 3, 2, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to primorial base.

Formula

a(n) = A129252(A380459(n)).

Prog

(PARI)
A129252(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(p)); 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); };
A380528(n) = A129252(A380459(n));

Crossrefs

Cf. A129252, A276086, A349394, A380459, A380468 (positions of 1's), A380529 [= a(A005117(n))], A380530 (positions of records).

Sequence in context: A264990 A277315 A277326 * A050431 A051574 A029386

Adjacent sequences: A380525 A380526 A380527 * A380529 A380530 A380531

Keyword

nonn

Author

Antti Karttunen, Feb 09 2025

Status

approved