A392858 a(n) = A028234(A276086(n)), where the A276086 is the primorial base exp-function, and A028234 completely removes the smallest prime factor of its argument.

1, 1, 1, 3, 1, 9, 1, 5, 5, 15, 5, 45, 1, 25, 25, 75, 25, 225, 1, 125, 125, 375, 125, 1125, 1, 625, 625, 1875, 625, 5625, 1, 7, 7, 21, 7, 63, 7, 35, 35, 105, 35, 315, 7, 175, 175, 525, 175, 1575, 7, 875, 875, 2625, 875, 7875, 7, 4375, 4375, 13125, 4375, 39375, 1, 49, 49, 147, 49, 441, 49, 245, 245, 735, 245, 2205, 49

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..16170

Index entries for sequences related to primorial base.

Formula

a(n) | A324895(n).

Prog

(PARI)
A028234(n) = { my(f=factor(n)); if(#f~, f[1, 1] = 1); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A392858(n) = A028234(A276086(n));
(PARI) A392858(n) = { my(m=1, p=2, e=0); while(n, if(n%p, if(e, m *= p^(n%p), e++)); n = n\p; p = nextprime(1+p)); (m); };

Crossrefs

Cf. A028234, A276086, A324895.

Cf. A060735 (positions of 1's after the initial one), A392613 [k such that a(k) | k].

Sequence in context: A317202 A355442 A331732 * A197259 A200006 A388957

Adjacent sequences: A392855 A392856 A392857 * A392859 A392860 A392861

Keyword

nonn,base

Author

Antti Karttunen, Jan 25 2026

Status

approved