A391927 Numbers k for which A373842(k) >= k, where A373842 is the arithmetic derivative of the primorial base log-function.

5, 7, 11, 13, 17, 19, 21, 23, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 71, 73, 76, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 99, 101, 102, 103, 104, 106, 107, 109, 111, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 127

Offset

1,1

Links

Table of n, a(n) for n=1..76.

Formula

{k such that A003415(A276085(k)) >= k}.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };
is_A391927(n) = (A003415(A276085(n))>=n);

Crossrefs

Cf. A003415, A276085, A373842.

After the initial 5, conjectured to be the complement of A373847.

Cf. A391938 (subsequence).

Sequence in context: A384322 A256387 A113909 * A391938 A111906 A348471

Adjacent sequences: A391924 A391925 A391926 * A391928 A391929 A391930

Keyword

nonn

Author

Antti Karttunen, Jan 15 2026

Status

approved