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

Author

Michel Lagneau, Jun 26 2014

Keywords

• nonn

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).

Examples

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

Links

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

Crossrefs

Cf. A094479, A193411, A185077.

Programs

Mathematica

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