cp's OEIS Frontend

A328252 Numbers that are not squarefree, but whose arithmetic derivative (A003415) is.

%I A328252 #9 Oct 11 2019 16:56:08
%S A328252 9,18,25,45,49,63,75,90,98,117,121,126,147,150,153,169,171,175,198,
%T A328252 234,242,245,261,279,289,294,315,325,333,338,342,350,361,363,369,387,
%U A328252 414,423,425,450,475,477,490,495,507,522,529,539,550,558,575,578,603,605,630,637,639,650,657,666,711,722,726,735,738,774,775,801
%N A328252 Numbers that are not squarefree, but whose arithmetic derivative (A003415) is.
%H A328252 Antti Karttunen, <a href="/A328252/b328252.txt">Table of n, a(n) for n = 1..10000</a>
%e A328252 18 = 2 * 3^2 is not squarefree, but its arithmetic derivative A003415(18) = 21 = 3*7 is, thus 18 is included in this sequence.
%o A328252 (PARI)
%o A328252 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328252 isA328252(n) = (!issquarefree(n) && issquarefree(A003415(n)));
%o A328252 (PARI)
%o A328252 A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i,2]>=f[i,1],return(0), s += f[i, 2]/f[i, 1])); (n*s));
%o A328252 A328248(n) = { my(k=1); while(n && !issquarefree(n), k++; n = A003415checked(n)); (!!n*k); };
%o A328252 isA328252(n) = (2==A328248(n));
%Y A328252 Cf. A003415, A328253.
%Y A328252 Row 3 of array A328250. Positions of 2's in A328248.
%Y A328252 Setwise difference A328234 \ A005117. Intersection of A013929 and A328234.
%K A328252 nonn
%O A328252 1,1
%A A328252 _Antti Karttunen_, Oct 11 2019