A377871 - OEIS

%I #19 Nov 19 2024 17:24:15

%S 2,3,5,6,7,10,11,13,14,17,18,19,22,23,26,29,30,31,34,37,38,41,42,43,

%T 45,46,47,50,53,58,59,61,62,63,66,67,70,71,73,74,75,78,79,82,83,86,89,

%U 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

%N 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.

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

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

%C From _Antti Karttunen_, Nov 17 2024: (Start)

%C 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.

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

%C (End)

%H Antti Karttunen, <a href="/A377871/b377871.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

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

%o (PARI) \\ See A377870.

%Y Intersection of A048103 and A377869.

%Y Sequence A276087 sorted into ascending order.

%Y Cf. A377870 (characteristic function).

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

%Y Cf. A006862, A143293, A276086, A376416.

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 10 2024