A347931 Nonprime numbers that divide their second arithmetic derivative.

1, 4, 8, 16, 24, 27, 48, 54, 64, 108, 128, 162, 168, 256, 320, 324, 432, 512, 704, 729, 864, 1024, 1134, 1728, 2048, 2160, 2187, 2192, 2916, 3125, 3456, 4096, 4752, 5120, 5832, 6250, 6912, 11664, 12500, 13824, 14580, 14796, 16384, 18750, 19683, 23328, 27648

Offset: 1

Author

Alois P. Heinz, Oct 15 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..250
• Wikipedia, Arithmetic derivative

Crossrefs

Cf. A000040, A003415, A018252, A068346, A348284.

Programs

Maple

d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
q:= n-> not isprime(n) and irem(d(d(n)), n)=0:
select(q, [$1..30000])[];  # Alois P. Heinz, Oct 15 2021

Formula

{ A348284 } minus { A000040 }.

{ A018252 } intersect { A348284 }.