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A348329
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Numbers k such that k' = k'', where ' is the arithmetic derivative.
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1
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OFFSET
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1,3
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COMMENTS
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For n > 2, a(n) is such that a(n)' = p^p for some prime p. So A051674 is a subsequence. - David A. Corneth, Oct 13 2021
If p > 2 and p^p-2 are both primes (i.e., p is an odd prime term of A100408), then 2*(p^p-2) is a term. Terms of this type are 1647082 and 3956839311320627178247954, corresponding to p = 7 and 19 respectively. - Amiram Eldar, Oct 13 2021
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LINKS
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FORMULA
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MAPLE
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isA348329 := proc(n)
local d ;
true ;
else
false;
end if;
end proc:
for n from 0 do
if isA348329(n) then
print(n) ;
end if;
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MATHEMATICA
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d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[0, 2.5*10^6], d[#] == d[d[#]] &] (* Amiram Eldar, Oct 13 2021 *)
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PROG
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(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
(Python)
from sympy import factorint
from itertools import count, islice
def ad(n): return 0 if n<2 else sum(n*e//p for p, e in factorint(n).items())
def agen(): yield from (k for k in count(0) if (adk:=ad(k)) == ad(adk))
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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