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A289740 Prime powers P for which the number of modulo P residues among sums of three sixth powers is less than P. 3
7, 8, 9, 13, 16, 19, 27, 31, 32, 49, 64, 81, 128, 169, 243, 256, 343, 361, 512, 729, 961, 1024, 2048, 2187, 2197, 2401, 4096, 4489, 6241, 6561, 6859, 8192, 16384, 16807, 19321, 19683, 28561, 29791, 32768, 49729, 59049, 65536, 117649, 130321, 131072, 177147 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: the largest prime in the sequence is 31. (If this is true, then the next terms after 32768 are 49729, 59049, and 65536.)

Every number > 4 that is a power of 2, 3, or 7 is in the sequence.

If any prime power P = p^k (where p is prime and k >= 1) is in the sequence, then so is p^j for all j > k.

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 1..56 (based on b-file for A289631 from Giovanni Resta)

EXAMPLE

5 is not in the sequence because (j^6 + k^6 + m^6) mod 5, where j, k, and m are integers, can take on all 5 values 0..4.

7 is in the sequence because (j^6 + k^6 + m^6) mod 7 can take on only 4 values (0..3), not 7.

14 is not in the sequence because -- although (j^6 + k^6 + m^6) mod 14 can take on only the 8 (not 14) values 0, 1, 2, 3, 7, 8, 9, and 10 -- 14 is not a prime power.

CROSSREFS

Subsequence of A289631 (similar sequence for sums of two sixth powers).

Cf. A289760 (similar sequence for sums of four sixth powers).

Sequence in context: A297257 A296698 A297131 * A289760 A241289 A037369

Adjacent sequences:  A289737 A289738 A289739 * A289741 A289742 A289743

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Jul 10 2017

EXTENSIONS

a(40)-a(46) added (based on b-file for A289631 from Giovanni Resta) by Jon E. Schoenfield, Jul 15 2017

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)