%I #13 Oct 08 2019 22:25:03

%S 7,10,18,21,25,38,46,65,77,98,129,170,205,217,254,361,414,426,462,493,

%T 501,529,718,753,982,998,1141,1362,1501,1502,2041,2045,2077,2105,2257,

%U 2285,2869,2933,2998,3102,3133,3706,4066,4078,4309,4497,4885,5213,5214,5461,5837,6363,6410,6546,6649,6749,6901,6913,6937,6953,7011

%N Numbers such that zero or more applications of A003415 (arithmetic derivative) will yield 7.

%C Union of {7} with those terms of k of A099308 for which A327968(k) = 7.

%H Antti Karttunen, <a href="/A328117/b328117.txt">Table of n, a(n) for n = 1..10000</a>

%H Antti Karttunen, <a href="/A328117/a328117.txt">Terms computed up to a(627664) = 4294966334; (all terms in range 1 .. 2^32)</a>

%e a(4) = 21 is included as A003415(A003415(21)) = 7.

%e a(627664) = 4294966334 (= 2^32 - 962) is included as A003415^(14)(4294966334) = 7. Note that A327966(4294966334) = 16.

%o (PARI)

%o 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 isA328117(n) = { while((n>7), n = A003415checked(n)); (7==n); };

%Y Cf. A003415, A099308, A327966, A327968, A327977, A328115.

%K nonn

%O 1,1

%A _Antti Karttunen_, Oct 06 2019