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

Offset: 1

Author

Zhao Hui Du, May 25 2023

Keywords

• nonn

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.

Examples

			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

Cf. A246547.