A328320 Numbers for which A328311(n) = 1 + A051903(A003415(n)) - A051903(n) is zero (including 1 as the initial term).

1, 2, 3, 5, 7, 8, 9, 11, 13, 17, 18, 19, 23, 24, 25, 29, 31, 32, 37, 40, 41, 43, 45, 47, 49, 53, 56, 59, 61, 63, 67, 71, 72, 73, 75, 79, 81, 83, 88, 89, 90, 96, 97, 98, 101, 103, 104, 107, 109, 113, 117, 120, 121, 125, 126, 127, 128, 131, 136, 137, 139, 147, 149, 150, 151, 152, 153, 157, 160, 162, 163, 167, 168, 169

Offset: 1

Author

Antti Karttunen, Oct 13 2019

Keywords

• nonn

Comments

After 1, the numbers whose "degree" (maximal exponent, A051903) is decremented by one when arithmetic derivative (A003415) is applied to them.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A003415, A051903, A328302, A328310.

Indices of zeros in A328311.

Cf. A328321 (complement), A328252 (a subsequence).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
A328311(n) = if(n<=1,0,1+(A051903(A003415(n)) - A051903(n)));
isA328320(n) = (0==A328311(n));