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A349485
Moran numbers whose arithmetic derivative is also a Moran number (A001101).
0
18, 27, 153, 803, 1101, 1503, 1926, 3070, 3077, 3546, 4577, 6246, 6315, 8717, 10566, 11646, 14093, 15310, 15426, 18456, 24936, 30617, 33576, 34326, 43079, 50418, 59026, 62004, 69781, 71009, 71802, 72587, 74616, 77593, 80118, 94056, 110138, 111546, 112626, 113166
OFFSET
1,1
COMMENTS
Conjecture: The sequence is infinite.
EXAMPLE
18 = A001101(1) and 18' = 21 = A001101(2), so 18 is a term.
153 = A001101(13) and 153' = 111 = A001101(8), so 153 is a term.
MATHEMATICA
moranQ[n_] := PrimeQ[n / Plus @@ IntegerDigits[n]]; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[120000], And @@ moranQ /@ {#, d[#]} &] (* Amiram Eldar, Nov 20 2021 *)
PROG
(Magma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]]) >; moran:=func<n|n mod &+Intseq(n) eq 0 and IsPrime(n div &+Intseq(n))>; [n:n in [2..114000]| moran(n) and moran(Floor(f(n)))];
CROSSREFS
Cf. A001101 (Moran number), A003415 (arithmetic derivative).
Sequence in context: A279108 A038632 A138336 * A166630 A154920 A094224
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Nov 20 2021
STATUS
approved