A392873 Nonsquarefree numbers k such that A276086(A003415(k)) <= k, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

9, 28, 108, 112, 136, 189, 212, 225, 236, 289, 361, 441, 475, 800, 961, 1544, 1800, 1884, 1940, 2132, 2308, 2348, 2524, 2655, 3501, 3771, 3860, 4225, 5725, 6921, 9024, 9936, 11449, 11552, 11881, 12221, 12769, 14027, 16129, 16296, 17797, 18769, 18888, 19133, 19321, 20020, 20024, 20360, 20493, 20772, 21450, 22491

Offset

1,1

Comments

It is conjectured that there are no common terms with A370115.

Of the 10000 initial terms, 4873 are in A371083 (in A048103), 1503 are in A080364, 1331 are in the intersection of A080364 and A048103, and 876 are in A392868 (in A391845), of which 704 are also in A048103.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base.

Formula

{k such that A008966(k) = 0 and A327859(k) <= k}.

Prog

(PARI) is_A392873(n) = if(issquarefree(n), 0, my(f=factor(n), u = n*sum(i=1, #f~, f[i, 2]/f[i, 1]), m=1, p=2); while(u, m *= (p^(u%p)); if(m>n, return(0)); u \= p; p = nextprime(1+p)); (1));

Crossrefs

Intersection of A013929 and A392867.

Cf. A008966, A048103, A080364, A327859, A370115, A371083, A392868, A393067.

Sequence in context: A053819 A294287 A349547 * A085292 A198059 A181090

Adjacent sequences: A392870 A392871 A392872 * A392874 A392875 A392876

Keyword

nonn

Author

Antti Karttunen, Feb 01 2026

Status

approved