A194769 Sum of distinct nonzero sixth powers.

1, 64, 65, 729, 730, 793, 794, 4096, 4097, 4160, 4161, 4825, 4826, 4889, 4890, 15625, 15626, 15689, 15690, 16354, 16355, 16418, 16419, 19721, 19722, 19785, 19786, 20450, 20451, 20514, 20515, 46656, 46657, 46720, 46721, 47385, 47386, 47449, 47450, 50752, 50753, 50816

Offset: 1

Author

Charles R Greathouse IV, Sep 02 2011

Keywords

• nonn
• easy

Comments

See A001661 for a proof of the formula. - M. F. Hasler, May 15 2020

From Peter Munn, Aug 02 2023: (Start)

11146309947 = A001661(6) 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(86) = 134067 = A364637(6).

If we tightened the sequence requirement so that the sum was of more than one 6th power, we would remove exactly 30 6th powers from the terms: row 6 of A332065 indicates which 6th powers would remain.

(End)

Links

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

Crossrefs

Cf. A001014, A001661, A332065, A364637.

A217846 is a subsequence.

Cf. A003997, A003999, A194768 (analogs for 3rd, 4th and 5th powers).

Programs

PARI

upto(lim)={
    lim\=1;
    my(v=List(),P=prod(n=1,lim^(1/6),1+x^(n^6),1+O(x^(lim+1))));
    for(n=1,lim,if(polcoeff(P,n),listput(v,n)));
    Vec(v)
}

Formula

For n > 9108736851, a(n) = n + 2037573096.

Extensions

More terms from David A. Corneth, Apr 21 2020

Name qualified by Peter Munn, Aug 02 2023