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

Author

Marius A. Burtea, May 03 2023

Keywords

• nonn

Comments

Sophie Germain primes p that are not Lucasian primes (A103579) are terms because p' = 1 = A224486(1).

Examples

			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.
		

Crossrefs

Cf. A003415, A103579, A224486.

Programs

Magma

czn:=func; f:=func; [n:n in [2..5000]|czn(n) and czn(Floor(f(n)))];

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 *)