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A363287

Numbers which cannot be written as the sum of 4 distinct proper prime powers (A246547).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 57, 59, 62, 63, 66, 67, 68, 73, 75, 80, 90, 95, 107, 134, 135, 136, 140, 145, 151, 152, 256, 2040, 340473

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OFFSET

1,2

COMMENTS

A proper prime power is an integer which is at least the 2nd power of a prime, such as 4, 8, 9, 16, 25, 27, as in A246547.

It is likely that all numbers above 162 can be written as the sum of 5 distinct proper prime powers.

a(72)=340473, a(73)=3881313, a(74)=4657401 and a(75) >= 10^9, if it exists.

LINKS

Table of n, a(n) for n=1..72.

EXAMPLE

The smallest integer which can be written as the sum of 4 proper prime powers is 37 = 4+8+9+16 so a(n)=n for n <= 36 and a(37) = 38.

CROSSREFS