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

1,2

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

Cf. A246547.

Sequence in context: A273886 A258068 A273885 * A174670 A212554 A178772

Adjacent sequences: A363284 A363285 A363286 * A363288 A363289 A363290

Keyword

nonn

Author

Zhao Hui Du, May 25 2023

Status

approved