A377871 Numbers k such that neither k nor A276085(k) has divisors of the form p^p, where A276085 is fully additive with a(p) = p#/p.

2, 3, 5, 6, 7, 10, 11, 13, 14, 17, 18, 19, 22, 23, 26, 29, 30, 31, 34, 37, 38, 41, 42, 43, 45, 46, 47, 50, 53, 58, 59, 61, 62, 63, 66, 67, 70, 71, 73, 74, 75, 78, 79, 82, 83, 86, 89, 90, 94, 97, 98, 99, 101, 102, 103, 105, 106, 107, 109, 110, 113, 114, 117, 118, 122, 125, 126, 127, 130, 131, 134, 137, 138, 139, 142

Offset: 1

Author

Antti Karttunen, Nov 10 2024

Keywords

• nonn

Comments

Range of A276087, where A276087(n) = A276086(A276086(n)) [the twofold application of the primorial base exp-function].

A276087(0) = 2, and for n >= 0, A276087(A143293(n)) = A000040(n+2), therefore all primes are included.

From Antti Karttunen, Nov 17 2024: (Start)

Even semiprimes > 4 form a subsequence, because A006862 (Euclid numbers) is a subsequence of A048103. Note that A276087(A376416(n)) = A276086(A006862(n)) = A100484(1+n). On the other hand, none of the odd semiprimes, A046315, occur here, because they are all included in A369002, and thus in A377873. Similarly, A276092 after its initial 1 is a subsequence, because A057588 (Kummer numbers) is also a subsequence of A048103.

For k=1..6, there are 6, 52, 486, 4775, 46982, 467372 terms <= 10^k. Question: Does this sequence have an asymptotic density?

(End)

Examples

			A276087(A002110(10)) = A276086(A276086(A002110(10))) = A276086(A000040(10+1)) = A276086(31) = 14, therefore 14 is included in this sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primorial base

Crossrefs

Intersection of A048103 and A377869.

Sequence A276087 sorted into ascending order.

Cf. A377870 (characteristic function).

Subsequences: A000040, A100484 (after its initial 4), A276092 (after its initial 1).

Cf. A006862, A143293, A276086, A376416.

Programs

PARI

\\ See A377870.