A244344 Numbers such that the largest prime factor equals the sum of the 4th power of the other prime factors.

582, 1164, 1746, 2328, 3492, 4656, 5238, 6410, 6984, 9312, 10476, 12820, 13968, 15714, 18624, 20952, 25640, 27936, 31428, 32050, 33838, 37248, 41904, 47142, 51280, 55872, 56454, 62856, 64100, 67676, 74496, 83808, 94284, 102560, 111744, 112908, 125712, 128200

Offset

1,1

Comments

Observation: it seems that the prime divisors of a majority of numbers n are of the form {2, p, q} with q = 2^4 + p^4, but there exists more rarely odd numbers with more prime divisors (example from Michel Marcus: 3955413 = 3*7*11*17123).

Links

Amiram Eldar, Table of n, a(n) for n = 1..1500

Example

582 is in the sequence because the prime divisors of 582 are 2, 3 and 97 => 2^4 + 3^4 = 97.

Mathematica

fpdQ[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]}, Max[f]-Total[Most[f]^4]==0]; Union[Select[Range[2, 5*10^5], fpdQ]]

Crossrefs

Cf. A094479, A193411, A185077.

Sequence in context: A172883 A260541 A162705 * A059468 A350663 A122694

Adjacent sequences: A244341 A244342 A244343 * A244345 A244346 A244347

Keyword

nonn

Author

Michel Lagneau, Jun 26 2014

Status

approved