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A194768
Sum of distinct positive fifth powers.
5
1, 32, 33, 243, 244, 275, 276, 1024, 1025, 1056, 1057, 1267, 1268, 1299, 1300, 3125, 3126, 3157, 3158, 3368, 3369, 3400, 3401, 4149, 4150, 4181, 4182, 4392, 4393, 4424, 4425, 7776, 7777, 7808, 7809, 8019, 8020, 8051, 8052, 8800, 8801, 8832, 8833, 9043, 9044, 9075, 9076
OFFSET
1,2
COMMENTS
From Peter Munn, Aug 02 2023: (Start)
67898771 = A001661(5) is the largest number not in the sequence.
After a(1) = 1, the next term that is in all the analogous sequences for smaller powers is a(35) = 7809 = A364637(5).
If we tightened the sequence requirement so that the sum was of more than one 5th power, we would remove exactly 24 5th powers from the terms: row 5 of A332065 indicates which 5th powers would remain.
(End)
FORMULA
For n > 53986089, a(n) = n + 13912682. [Charles R Greathouse IV, Sep 02 2011]
MAPLE
N:= 2*10^4: # to get all terms <= N
S:= {0}:
for i from 1 while i^5 <= N do
S:= select(`<=`, map(`+`, S, i^5), N) union S
od:
sort(convert(S minus {0}, list)); # Robert Israel, Jun 26 2019
PROG
(PARI) upto(lim)={
lim\=1;
my(v=List(), P=prod(n=1, lim^(1/5), 1+x^(n^5), 1+O(x^(lim+1))));
for(n=1, lim, if(polcoeff(P, n), listput(v, n)));
Vec(v)
}; \\ Charles R Greathouse IV, Sep 02 2011
CROSSREFS
Cf. A000584 (5th powers), A001661, A332065, A364637.
Cf. A003997, A003999, A194769 (analogs for 3rd, 4th and 6th powers).
A217845 is a subsequence.
Sequence in context: A134844 A151983 A022402 * A217845 A067010 A332923
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name qualified by Peter Munn, Aug 02 2023
STATUS
approved