A194768 Sum of distinct positive fifth powers.

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

Author

Charles R Greathouse IV, Sep 02 2011

Keywords

• nonn

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)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A000584 (5th powers), A001661, A332065, A364637.

Cf. A003997, A003999, A194769 (analogs for 3rd, 4th and 6th powers).

A217845 is a subsequence.

Programs

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

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

Formula

For n > 53986089, a(n) = n + 13912682. [Charles R Greathouse IV, Sep 02 2011]

Extensions

Name qualified by Peter Munn, Aug 02 2023