A328320 - OEIS

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

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OFFSET

1,2

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

PROG

(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)));