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A380474 Numbers k such that A380459(k) has no divisors of the form p^p, while A003415(k) has such a divisor or is 0.

%I A380474 #26 Feb 03 2025 19:56:31
%S A380474 1,158,482,698,914,1238,1346,1454,1994,2102,2426,2642,2858,2966,3398,
%T A380474 3506,3722,4262,4478,4586,4694,5234,5342,5666,5774,6098,6638,6746,
%U A380474 7286,7394,7934,8042,8258,9014,9122,9446,9662,9986,10202,10418,10958,11282,11498,11714,12146,12686,12794,12902
%N A380474 Numbers k such that A380459(k) has no divisors of the form p^p, while A003415(k) has such a divisor or is 0.
%C A380474 Because all terms k of A380468 are squarefree, they are also in A048103, so A003415(k) is outside of A048103 only if k is in A327934 or k = 1.
%C A380474 Like A380478, also this (after the initial 1) is a subsequence of A039956. The first three terms k with A001222(k) > 2 are: 11362082, 16782482, 20965982.
%C A380474 Contains 2*A141964 as a subsequence, because all primes p congruent to 25 mod 27 are also congruent to 1 mod 6, therefore A276086(p) is a nonmultiple of 3 in those cases and thus coprime with A276086(2) = 3.
%C A380474 In contrast, neither all 2*(primes congruent to 3123 mod 3125) nor all 2*(primes congruent to (7^7)-2 mod 7^7, like 1647082) are present. The missing ones are those for which A276086(p) is a multiple of 9, i.e., when p is in A047257.
%H A380474 Antti Karttunen, <a href="/A380474/b380474.txt">Table of n, a(n) for n = 1..20000</a>
%H A380474 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%o A380474 (PARI) is_A380474(n) = (A380467(n) && !A368915(n));
%Y A380474 Cf. A003415, A047257, A048103, A141964, A276086, A358215, A380459.
%Y A380474 Intersection of A380468 and ({1} U A327929), or equally of A380478 and ({1} U A327934).
%Y A380474 After initial 1, a subsequence of A039956.
%K A380474 nonn
%O A380474 1,2
%A A380474 _Antti Karttunen_, Feb 02 2025