A392867 Numbers k such that A276086(A003415(k)) <= k, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

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

Offset

1,2

Comments

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

Links

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

Index entries for sequences related to primorial base.

Formula

{k such that A327859(k) <= k}.

A393057(a(n)) = n.

Prog

(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));

Crossrefs

Cf. A003415, A276086, A327859, A393056, A393057 (left inverse), A393067 (characteristic function).

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

Cf. also A392601, A392605, A392869.

Sequence in context: A047489 A375488 A196499 * A035061 A302403 A096738

Adjacent sequences: A392864 A392865 A392866 * A392868 A392869 A392870

Keyword

nonn

Author

Antti Karttunen, Jan 27 2026

Status

approved