A392869 Numbers k for which A003415(k) >= A276085(k), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 2, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 28, 30, 32, 36, 40, 42, 45, 48, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120, 125, 126, 128, 135, 140, 144, 147, 150, 160, 162, 168, 175, 176, 180, 189, 192, 196, 198, 200, 210, 216, 220, 224, 225, 240, 243, 245, 250, 252, 256

Offset

1,2

Links

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

Formula

{k such that A276085(A380459(k)) >= A276085(k)}.

Prog

(PARI) is_A392869(k) = (A003415(k)>=A276085(k));
(PARI) is_A392869(n) = { my(f = factor(n), ad=n*sum(i=1, #f~, f[i, 2]/f[i, 1]), pr=1, q=1, s=0); for(k=1, #f~, forprime(p = nextprime(1+q), f[k, 1]-1, pr *= p; if(pr > ad, return(0)); q = p); s += f[k, 2]*pr; if(s > ad, return(0))); (1); };

Crossrefs

Cf. A003415, A276085, A380459.

Subsequences: A369650, A373490.

Cf. also A392601.

Sequence in context: A118672 A100417 A333337 * A070089 A371169 A353759

Adjacent sequences: A392866 A392867 A392868 * A392870 A392871 A392872

Keyword

nonn

Author

Antti Karttunen, Jan 28 2026

Status

approved