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A290135
Numbers that are the sum of two proper prime powers (A246547).
1
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
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}]]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 20 2017
STATUS
approved