A392868 Numbers k such that A276086(A003415(k)) <= k and the least prime not dividing A003415(k) is equal to the least prime dividing k, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

1, 2, 10, 15, 30, 35, 58, 62, 87, 93, 118, 155, 161, 177, 185, 246, 282, 290, 305, 371, 422, 478, 482, 498, 581, 633, 717, 723, 838, 842, 1055, 1205, 1257, 1263, 1631, 1841, 2105, 2189, 2442, 2766, 2778, 2802, 3018, 3054, 3101, 3590, 3938, 4234, 4454, 4499, 4618, 4622, 4678, 4682, 4694, 4702, 4742, 5005, 5042, 5098

Offset

1,2

Comments

The terms in this sequence are considerably rarer than in either of A391845 or A392867. Also the scatter plot is noticeably curvy, even though both A391845 AND A392867 seem to have quite even growth rates, at least for their initial 10000 terms. Compare also the scatter plots of A393056 - A393058.

Among the 25367 initial terms, there are 22975 squarefree terms (in A005117), 2142 terms in A371083, and only 250 terms in A100716. Of those 25637 terms, the terms common with A392601 (also, with A373490) are just these five: 1, 2, 10, 15, 5005. See A369650.

Links

Antti Karttunen, Table of n, a(n) for n = 1..25367; all terms less than 2^34

Index entries for sequences related to primorial base.

Formula

{k such that A053669(A003415(k)) == A020639(k) and A276086(A003415(k)) <= k}.

A393058(a(n)) = n.

Prog

(PARI) is_A392868(n) = (A391844(n) && is_A392867(n));
(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p)));
is_A392868(n) = if(n<3 || isprime(n), (n && n<3), my(f=factor(n), u = n*sum(i=1, #f~, f[i, 2]/f[i, 1]), m=1, p=2); if(A053669(u)!=f[1, 1], return(0)); while(u, m *= (p^(u%p)); if(m>n, return(0)); u \= p; p = nextprime(1+p)); (1));

Crossrefs

Intersection of A391845 and A392867.

Cf. A003415, A020639, A053669, A276085, A276086, A370115 (probably subsequence), A373490, A369650, A392601, A393058 (left inverse), A393068 (characteristic function).

Cf. A005117, A100716, A371083.

Sequence in context: A391864 A391865 A369650 * A181474 A392607 A047187

Adjacent sequences: A392865 A392866 A392867 * A392869 A392870 A392871

Keyword

nonn,look

Author

Antti Karttunen, Jan 27 2026

Status

approved