A362140 Numbers k in A224486 for which the arithmetic derivative k' (A003415) is also in A224486.

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).

Links

Table of n, a(n) for n=1..57.

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

Cf. A003415, A103579, A224486.

Sequence in context: A193978 A224486 A163782 * A226793 A255747 A256264

Adjacent sequences: A362137 A362138 A362139 * A362141 A362142 A362143

Keyword

nonn

Author

Marius A. Burtea, May 03 2023

Status

approved