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.

1, 158, 482, 698, 914, 1238, 1346, 1454, 1994, 2102, 2426, 2642, 2858, 2966, 3398, 3506, 3722, 4262, 4478, 4586, 4694, 5234, 5342, 5666, 5774, 6098, 6638, 6746, 7286, 7394, 7934, 8042, 8258, 9014, 9122, 9446, 9662, 9986, 10202, 10418, 10958, 11282, 11498, 11714, 12146, 12686, 12794, 12902

Offset: 1

Author

Antti Karttunen, Feb 02 2025

Keywords

• nonn

Comments

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.

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.

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.

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A003415, A047257, A048103, A141964, A276086, A358215, A380459.

Intersection of A380468 and ({1} U A327929), or equally of A380478 and ({1} U A327934).

After initial 1, a subsequence of A039956.

Programs

PARI

is_A380474(n) = (A380467(n) && !A368915(n));