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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 (list; graph; refs; listen; history; text; internal format)
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):
select(q, [$1..250])[]; # Alois P. Heinz, Oct 15 2021
PROG
(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
isok(k) = !(ad(ad(k)) % k); \\ Michel Marcus, Oct 10 2021
CROSSREFS
Cf. A003415 (1st derivative), A068346 (2nd derivative).
Sequence in context: A307824 A081730 A162408 * A162721 A176176 A174090
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 09 2021
STATUS
approved

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Last modified April 17 07:13 EDT 2024. Contains 371756 sequences. (Running on oeis4.)