A185077 -id:A185077 - cp's OEIS frontend

A244637 Primes that are the sum of the squares of distinct primes.

13, 29, 53, 83, 173, 179, 199, 227, 293, 347, 367, 373, 419, 439, 463, 467, 487, 491, 541, 563, 569, 587, 607, 613, 617, 641, 653, 659, 709, 727, 733, 751, 809, 823, 827, 829, 853, 857, 877, 881, 919, 953, 971, 977, 991, 997, 1013, 1019, 1021, 1039, 1049

Offset: 1

Michel Marcus, Jul 03 2014

nonn

Primes in A048261.
Provide the prime factors of A185077.
A045637 is a subsequence.
There are only 368 primes not in this sequence, the largest being 12601. - Robert Israel, Jul 04 2014

			13 is in the sequence since it is prime and 13 = 2^2 + 3^2 (2 and 3 are distinct primes).

Vincenzo Librandi, Table of n, a(n) for n = 1..2870

Cf. A045637, A048261, A121518, A185077.

nn=10;s={0};Do[p=Prime[n];s=Union[s,s+p^2],{n,nn}];Select[s,(0<#<=Prime[nn]^2)&&PrimeQ[#]&] (* Michel Lagneau, Jul 03 2014 *)

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

Original entry on oeis.org

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

Michel Lagneau, Jun 26 2014

nonn

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).

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

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

Cf. A094479, A193411, A185077.

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

cp's OEIS Frontend

A244637 Primes that are the sum of the squares of distinct primes.

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