cp's OEIS Frontend

A327929 Numbers for which there is at least one such prime p that p^p divides the arithmetic derivative of n, A003415(n).

%I A327929 #12 Oct 01 2019 19:50:52
%S A327929 4,8,12,15,16,20,24,27,28,32,35,36,39,40,44,48,51,52,54,55,56,60,64,
%T A327929 68,72,76,80,81,84,87,88,91,92,95,96,100,104,108,111,112,115,116,119,
%U A327929 120,123,124,128,132,135,136,140,143,144,148,152,155,156,158,159,160,162,164,168,172,176,180,183,184,187,188,189,192,196,200
%N A327929 Numbers for which there is at least one such prime p that p^p divides the arithmetic derivative of n, A003415(n).
%C A327929 Numbers k such that A327928(k) = A129251(A003415(k)) is > 0, i.e., numbers whose arithmetic derivative is in A100716.
%C A327929 For all n, A003415(a(n)) is also present in this sequence and A003415(a(n)) = m * A327965(a(n)) for some m > 1.
%H A327929 Antti Karttunen, <a href="/A327929/b327929.txt">Table of n, a(n) for n = 1..30000</a>
%o A327929 (PARI)
%o A327929 A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
%o A327929 A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
%o A327929 A327928(n) = if(n<=1,0,A129251(A003415(n)));
%o A327929 isA327929(n) = (A327928(n)>0);
%Y A327929 Cf. A003415, A100716, A129251, A327965.
%Y A327929 Indices of nonzero terms in A327928.
%Y A327929 Cf. A099309, A327934 for subsequences.
%K A327929 nonn
%O A327929 1,1
%A A327929 _Antti Karttunen_, Oct 01 2019