A377989 Numbers k such that A003415(A276085(k)) has no p^p-factors, where A003415 is the arithmetic derivative, and A276085 is fully additive with a(p) = p#/p.

3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 17, 18, 19, 22, 23, 24, 26, 27, 29, 30, 31, 32, 36, 37, 38, 40, 41, 42, 43, 45, 47, 48, 50, 53, 54, 56, 59, 60, 61, 63, 64, 66, 67, 70, 71, 72, 73, 74, 75, 78, 79, 80, 82, 83, 84, 86, 88, 89, 90, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 110, 112, 113, 114, 117, 118, 120

Offset: 1

Author

Antti Karttunen, Nov 18 2024

Keywords

• nonn

Comments

Numbers k such that A373842(k) is in A048103.

Odd primes (A065091) are all present. See comment in A024451.

Examples

			A276085(1) = 0 and A276085(2) = 1, and as A003415(0) = A003415(1) = 0, and because 0 is a multiple of every number of the form p^p, with p prime, 1 and 2 are NOT included in this sequence.
A276085(3) = 2, A003415(2) = 1, and as 1 has no p^p-factors, 3 is included in this sequence.
A276085(34) = 30031 = A002110(1-1)+A002110(7-1) (34 = 2*17 = prime(1)*prime(7)), and because A003415(30031) = 568 = 2^2 * 2 * 71, with a factor of the form p^p, 34 is NOT included in this sequence.
		

Crossrefs

Cf. A003415, A024451, A048103, A065091 (subsequence), A276085, A359550, A368915, A373842, A377988 (characteristic function).

Subsequence of A377869. First terms there, but not present here are 2 and 34.

Programs

PARI

isA377989 = A377988;