A066846
Numbers of the form a^a + b^b, a >= b > 0.
Original entry on oeis.org
2, 5, 8, 28, 31, 54, 257, 260, 283, 512, 3126, 3129, 3152, 3381, 6250, 46657, 46660, 46683, 46912, 49781, 93312, 823544, 823547, 823570, 823799, 826668, 870199, 1647086, 16777217, 16777220, 16777243, 16777472, 16780341, 16823872, 17600759, 33554432
Offset: 0
28 is included because 28 = 1^1 + 3^3.
Cf.
A068145: primes of the form a^a + b^b.
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nn = 10; Select[Union[Flatten[Table[a^a + b^b, {a, nn}, {b, a, nn}]]], # <= nn^nn + 1 &] (* T. D. Noe, Nov 15 2012 *)
A218346
Numbers of the form a^a + b^b, with a > b > 0.
Original entry on oeis.org
5, 28, 31, 257, 260, 283, 3126, 3129, 3152, 3381, 46657, 46660, 46683, 46912, 49781, 823544, 823547, 823570, 823799, 826668, 870199, 16777217, 16777220, 16777243, 16777472, 16780341, 16823872, 17600759, 387420490, 387420493, 387420516, 387420745, 387423614, 387467145
Offset: 1
a(1) = 2^2 + 1^1 = 5,
a(2) = 3^3 + 1^1 = 28,
a(3) = 2^2 + 3^3 = 31.
Cf.
A068145: primes of the form a^a + b^b.
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N:= 10^12: # for terms <= N
S:= NULL:
for m from 1 do v:= m^m; if v > N then break fi; S:= S,v od:
sort(convert(select(`<=`,{seq(seq(S[i]+S[j],j=i+1..m-1),i=1..m-1)},N),list)); # Robert Israel, Aug 10 2020
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nn = 10; Select[Union[Flatten[Table[a^a + b^b, {a, nn}, {b, a + 1, nn}]]], # <= nn^nn + 1 &] (* T. D. Noe, Nov 15 2012 *)
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from itertools import count, takewhile
def aupto(lim):
pows = list(takewhile(lambda x: x < lim, (i**i for i in count(1))))
sums = (aa+bb for i, bb in enumerate(pows) for aa in pows[i+1:])
return sorted(set(s for s in sums if s <= lim))
print(aupto(387467145)) # Michael S. Branicky, May 28 2021
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