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A362140
Numbers k in A224486 for which the arithmetic derivative k' (A003415) is also in A224486.
0
2, 5, 6, 9, 14, 18, 29, 33, 41, 53, 54, 65, 69, 89, 113, 134, 141, 158, 173, 198, 209, 221, 233, 249, 278, 281, 293, 326, 329, 338, 393, 473, 506, 509, 545, 581, 593, 614, 629, 641, 653, 713, 729, 749, 761, 809, 846, 905, 950, 953, 965, 986, 1013, 1014, 1026, 1041, 1049
OFFSET
1,1
COMMENTS
Sophie Germain primes p that are not Lucasian primes (A103579) are terms because p' = 1 = A224486(1).
EXAMPLE
6 = A224486(4) and 6' = 5 = A224486(3), so 6 is a term.
9 = A224486(5) and 9' = 6 = A224486(4), so 9 is a term.
14 = A224486(6) and 14' = 9 = A224486(5), so 14 is a term.
MATHEMATICA
d[0] = d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); curzonQ[n_] := PowerMod[2, n, 2*n + 1] == 2*n; Select[Range[2, 1050], curzonQ[#] && curzonQ[d[#]] &] (* Amiram Eldar, May 05 2023 *)
PROG
(Magma) czn:=func<n|(2^n+1) mod (2*n+1) eq 0>; f:=func<n |n le 1 select 0 else
n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in
[1..#Factorisation(n)]])>; [n:n in [2..5000]|czn(n) and czn(Floor(f(n)))];
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius A. Burtea, May 03 2023
STATUS
approved