A377989 - OEIS

%I #11 Nov 18 2024 14:16:20

%S 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,

%T 40,41,42,43,45,47,48,50,53,54,56,59,60,61,63,64,66,67,70,71,72,73,74,

%U 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

%N 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.

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

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

%e 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.

%e A276085(3) = 2, A003415(2) = 1, and as 1 has no p^p-factors, 3 is included in this sequence.

%e 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.

%o (PARI) isA377989 = A377988;

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

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

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 18 2024