A225103 Numbers that can be represented as a sum of two distinct nontrivial prime powers in two or more ways.

36, 41, 57, 89, 113, 129, 130, 137, 153, 177, 185, 297, 305, 368, 370, 377, 410, 425, 537, 545, 561, 593, 633, 650, 657, 850, 857, 868, 873, 890, 969, 986, 1010, 1130, 1385, 1490, 1690, 1730, 1802, 1865, 1881, 1898, 1970, 2210, 2213, 2217, 2236, 2330, 2337

Offset

1,1

Comments

Indices of terms bigger than 1 in A225099.

Nontrivial prime powers are numbers of the form p^k where p is a prime number and k >= 2. That is, A025475 except the first term A025475(1) = 1.

Only 267 of the terms below 2^34 are odd.

Links

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

Example

36 = 32 + 4 = 27 + 9, so 36 is in the sequence.
41 = 32 + 9 = 25 + 16, so 41 is in the sequence.

Maple

N:= 10^4: # to get all terms <= N
PP:= [seq(seq(p^k, k=2..floor(log[p](N))), p = select(isprime, [2, seq(i, i=3..floor(sqrt(N)), 2)]))]:
npp:= nops(PP):
res:= {}: R:= 'R':
for i from 2 to npp do
  for j from 1 to i-1 do
    q:= PP[i]+PP[j];
    if assigned(R[q]) then res:= res union {q}
    else R[q]:= 1
    fi
od od:
sort(convert(res, list)); # Robert Israel, Feb 17 2017

Mathematica

nn = 2409; p = Sort[Flatten[Table[Prime[n]^i, {n, PrimePi[Sqrt[nn]]}, {i, 2, Log[Prime[n], nn]}]]]; Transpose[Sort[Select[Tally[Flatten[Table[p[[i]] + p[[j]], {i, Length[p] - 1}, {j, i + 1, Length[p]}]]], #[[1]] <= nn && #[[2]] > 1 &]]][[1]] (* T. D. Noe, Apr 29 2013 *)

Crossrefs

Cf. A025475, A225099, A225102.

Sequence in context: A344808 A295694 A295492 * A067372 A084147 A261258

Adjacent sequences: A225100 A225101 A225102 * A225104 A225105 A225106

Keyword

nonn

Author

Alex Ratushnyak, Apr 28 2013

Status

approved