A328117 Numbers such that zero or more applications of A003415 (arithmetic derivative) will yield 7.

7, 10, 18, 21, 25, 38, 46, 65, 77, 98, 129, 170, 205, 217, 254, 361, 414, 426, 462, 493, 501, 529, 718, 753, 982, 998, 1141, 1362, 1501, 1502, 2041, 2045, 2077, 2105, 2257, 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

Offset: 1

Author

Antti Karttunen, Oct 06 2019

Keywords

• nonn

Comments

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

Examples

			a(4) = 21 is included as A003415(A003415(21)) = 7.
a(627664) = 4294966334 (= 2^32 - 962) is included as A003415^(14)(4294966334) = 7. Note that A327966(4294966334) = 16.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Terms computed up to a(627664) = 4294966334; (all terms in range 1 .. 2^32)

Crossrefs

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

Programs

PARI

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