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

1,2

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).

Formula

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

Prog

(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)
}

Crossrefs

Cf. A001014, A001661, A332065, A364637.

A217846 is a subsequence.

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

Sequence in context: A255570 A255571 A151984 * A217846 A135124 A223590

Adjacent sequences: A194766 A194767 A194768 * A194770 A194771 A194772

Keyword

nonn,easy

Author

Charles R Greathouse IV, Sep 02 2011

Extensions

More terms from David A. Corneth, Apr 21 2020

Name qualified by Peter Munn, Aug 02 2023

Status

approved