A392873 - OEIS

%I #12 Feb 01 2026 21:50:35

%S 9,28,108,112,136,189,212,225,236,289,361,441,475,800,961,1544,1800,

%T 1884,1940,2132,2308,2348,2524,2655,3501,3771,3860,4225,5725,6921,

%U 9024,9936,11449,11552,11881,12221,12769,14027,16129,16296,17797,18769,18888,19133,19321,20020,20024,20360,20493,20772,21450,22491

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

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

%C 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.

%H Antti Karttunen, <a href="/A392873/b392873.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.

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

%o (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));

%Y Intersection of A013929 and A392867.

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

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 01 2026