A290135 Numbers that are the sum of two proper prime powers (A246547).

8, 12, 13, 16, 17, 18, 20, 24, 25, 29, 31, 32, 33, 34, 35, 36, 40, 41, 43, 48, 50, 52, 53, 54, 57, 58, 59, 64, 65, 68, 72, 73, 74, 76, 80, 81, 85, 89, 90, 91, 96, 97, 98, 106, 108, 113, 125, 128, 129, 130, 132, 133, 134, 136, 137, 141, 144, 145, 146, 148, 150, 152, 153, 155, 157, 160, 162, 170, 173, 174, 177, 178

Offset

1,1

Comments

Is 2213 the largest prime term that can be expressed as the sum of two proper prime powers in more than one way? - Altug Alkan, Jul 22 2017

Links

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

Formula

Exponents in expansion of (Sum_{k>=1} x^A246547(k))^2.

Example

13 is in the sequence because 13 = 2^2 + 3^2.

Maple

N:= 1000: # to get all terms <= N
P:= select(isprime, [$2..floor(sqrt(N))]):
PP:= {seq(seq(p^j, j=2..floor(log[p](N))), p=P)}:
A:= select(`<=`, {seq(seq(PP[i]+PP[j], j=1..i), i=1..nops(PP))}, N):
sort(convert(A, list)); # Robert Israel, Jul 21 2017

Mathematica

nmax = 180; f[x_] := Sum[Boole[PrimePowerQ[k] && PrimeOmega[k] > 1] x^k, {k, 1, nmax}]^2; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, nmax}]]

Crossrefs

Cf. A014091, A070049, A071330, A071331, A225102, A225103, A246547.

Sequence in context: A295782 A331801 A143813 * A225533 A143845 A270888

Adjacent sequences: A290132 A290133 A290134 * A290136 A290137 A290138

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 20 2017

Status

approved