A392867 - OEIS

%I #20 Feb 01 2026 10:52:44

%S 1,2,3,5,7,9,10,11,13,15,17,19,23,28,29,30,31,35,37,41,43,47,53,58,59,

%T 61,62,67,71,73,79,83,87,89,93,97,101,103,107,108,109,112,113,118,127,

%U 131,136,137,139,145,149,151,155,157,161,163,167,173,177,179,181,185,189,191,193,197,199,203,209,211,212,217

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

%C Only terms 1, 2, 10, 15, 28, 5005, 22491, 201096 occur among the initial 100000 terms of A392601.

%H Antti Karttunen, <a href="/A392867/b392867.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 A327859(k) <= k}.

%F A393057(a(n)) = n.

%o (PARI) is_A392867(n) = if(!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 Cf. A003415, A276086, A327859, A393056, A393057 (left inverse), A393067 (characteristic function).

%Y Subsequences: A000040, A369650, A370115, A392868, A392873 (nonsquarefree terms).

%Y Cf. also A392601, A392605, A392869.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 27 2026