A193411 -id:A193411 - cp's OEIS frontend

A130833 Sums of two or more distinct 4th powers of primes.

97, 641, 706, 722, 2417, 2482, 2498, 3026, 3042, 3107, 3123, 14657, 14722, 14738, 15266, 15282, 15347, 15363, 17042, 17058, 17123, 17139, 17667, 17683, 17748, 17764, 28577, 28642, 28658, 29186, 29202, 29267, 29283, 30962, 30978, 31043, 31059, 31587, 31603

Offset: 1

Jonathan Vos Post, Jul 21 2011

This is to cubes and A030078 as A192926 is to 4th powers and A030514. The subsequence of primes which are sums of two or more distinct 4th powers of primes begins 97, 641, 2417 (A193411).

The first term that arises in more than one way is 6539044 = 11^4 + 23^4 + 41^4 + 43^4 = 13^4 + 29^4 + 31^4 + 47^4. - Robert Israel, Apr 27 2020

			a(1) = 97 = 2^4 + 3^4.
a(2) = 641 = 2^4 + 5^4.
a(3) = 706 = 3^4 + 5^4.
a(4) = 722 = 2^4 + 3^4 + 5^4.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000040, A000583, A030514, A192926, A193411.

N:= 40000: # for all terms <= N
S1:= {}:
S2:= {}:
p:= 1:
do
  p:= nextprime(p);
  if p^4 > N then break fi;
  s:= p^4;
  S2:= S2 union select(`<=`,map(`+`,S1 union S2, s), N);
  S1:= S1 union {s};
od:
sort(convert(S2,list)); # Robert Israel, Apr 27 2020

nn=6; t = Sort@ Flatten@ Table[ n^4, {n, Prime@ Range@ nn}]; Select[Sort[
Plus @@@ Subsets[t, {2, nn}]], # < Prime[nn-1]^4 + Prime[nn]^4 &] (* Robert G. Wilson v, Jul 22 2011 *)

{A030078(i) + A030078(j) for i not equal to j} UNION {A030078(i) + A030078(j) + A030078(k) for i not equal to j not equal to k} UNION {A030078(i) + A030078(j) + A030078(k) + A030078(L) for i not equal to j not equal to k not equal to L}...

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

A130833 Sums of two or more distinct 4th powers of primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula