A393048 Composite numbers k such that k is >= A276085(A003415(k)), where A003415 is the arithmetic derivative and A276085 is fully additive with a(p) = p#/p.

4, 6, 8, 9, 12, 14, 15, 16, 20, 21, 25, 26, 27, 28, 32, 33, 35, 36, 38, 39, 44, 46, 48, 49, 50, 51, 52, 54, 55, 64, 65, 68, 76, 77, 81, 86, 87, 88, 91, 92, 94, 95, 99, 100, 108, 111, 112, 115, 116, 119, 122, 124, 125, 128, 135, 141, 143, 144, 146, 155, 158, 159, 160, 161, 164, 180, 183, 185, 187, 188, 189, 192, 196

Offset

1,1

Links

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

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_A393048(n) = (n>1 && !isprime(n) && (A276085(A003415(n)) <= n));

Crossrefs

Cf. A002808, A003415, A276085, A393049 (subsequence).

Cf. also A392869.

Sequence in context: A259315 A211771 A211772 * A353355 A231573 A327204

Adjacent sequences: A393045 A393046 A393047 * A393049 A393050 A393051

Keyword

nonn

Author

Antti Karttunen, Feb 06 2026

Status

approved