A392605 Numbers k such that A327860(k) <= k, where A327860 is the arithmetic derivative of the primorial base exp-function.

0, 1, 2, 6, 7, 8, 12, 30, 31, 32, 36, 60, 210, 211, 212, 213, 214, 216, 217, 218, 222, 240, 241, 242, 246, 270, 420, 421, 422, 426, 450, 630, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 2320, 2321, 2322, 2323, 2324, 2328, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2352, 2370, 2371, 2372

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..54334

Index entries for sequences related to primorial base.

Prog

(PARI)
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
is_A392605(k) = (k>=A327860(k));
(PARI) is_A392605(k) = { my(n=k, s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); if((s*m)>k, return(0)); n = n\p; p = nextprime(1+p)); ((s*m)<=k); };

Crossrefs

Cf. A327860.

Subsequences: A002110, A328110, A380527, A392606.

Sequence in context: A362462 A287321 A030366 * A048859 A026311 A063291

Adjacent sequences: A392602 A392603 A392604 * A392606 A392607 A392608

Keyword

nonn,base

Author

Antti Karttunen, Jan 23 2026

Status

approved