cp's OEIS Frontend

A358215 Numbers k for which there is no prime p such that p^p divides the arithmetic derivative of k, A003415(k).

%I A358215 #21 Feb 22 2024 20:08:24
%S A358215 2,3,5,6,7,9,10,11,13,14,17,18,19,21,22,23,25,26,29,30,31,33,34,37,38,
%T A358215 41,42,43,45,46,47,49,50,53,57,58,59,61,62,63,65,66,67,69,70,71,73,74,
%U A358215 75,77,78,79,82,83,85,86,89,90,93,94,97,98,99,101,102,103,105,106,107,109,110,113,114,117,118,121,122,125
%N A358215 Numbers k for which there is no prime p such that p^p divides the arithmetic derivative of k, A003415(k).
%C A358215 Numbers k such that A003415(k) is in A048103.
%H A358215 Antti Karttunen, <a href="/A358215/b358215.txt">Table of n, a(n) for n = 1..10000</a>
%o A358215 (PARI)
%o A358215 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A358215 A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };
%o A358215 A368915(n) = ((n>1)&&A359550(A003415(n)));
%o A358215 isA358215(n) = A368915(n);
%Y A358215 Complement of {1} U A327929. Positions of 0's in A341996 (after the two initial zeros). Positions of 1's in A341997.
%Y A358215 Subsequence of A048103.
%Y A358215 Subsequences: A099308 (apart from its two initial terms), A328393, A358221.
%Y A358215 Cf. A003415, A327934, A351088, A359550, A368915 (characteristic function).
%K A358215 nonn
%O A358215 1,1
%A A358215 _Antti Karttunen_, Nov 24 2022