

A348284


Numbers k such that k  k" where k" is the 2nd arithmetic derivative of k.


2



1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 17, 19, 23, 24, 27, 29, 31, 37, 41, 43, 47, 48, 53, 54, 59, 61, 64, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 108, 109, 113, 127, 128, 131, 137, 139, 149, 151, 157, 162, 163, 167, 168, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233
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OFFSET

1,2


COMMENTS

As 1" = 0 and p" = 0 when p is prime, 1 and every prime are terms, hence A008578 is a subsequence.  Bernard Schott, Oct 12 2021


LINKS



EXAMPLE

8 is in the sequence since 8" = 16 and 8  16.


MAPLE

d:= n> n*add(i[2]/i[1], i=ifactors(n)[2]):
q:= n> is(irem(d(d(n)), n)=0):


PROG

(PARI) ad(n) = vecsum([n/f[1]*f[2]f<factor(n+!n)~]); \\ A003415


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



