A344023 Numbers of the form p_1^1 + p_2^2 + ... + p_k^k where p_1 < p_2 < ... < p_k are distinct primes.

0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 27, 28, 29, 31, 37, 41, 43, 47, 51, 52, 53, 54, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 123, 124, 126, 127, 128, 131, 136, 137, 139, 149, 151, 157, 163, 167, 171, 172, 173, 174, 176, 179, 180, 181, 191, 193, 197, 199

Offset: 1

Author

Bernard Schott, May 07 2021

Keywords

• nonn

Comments

Also, ordered distinct values taken by terms of A343300.

Primes form the subsequence corresponding to k = 1.

Examples

			0 is a term  because it is the empty sum.
11 is a term because 11 = 11^1 is prime and also 11 = 2^1 + 3^2.
52 is a term because 3^1 + 7^2 = 52.
1382 is a term because 2^1 + 7^2 + 11^3 = 13^1 +37^2 = 1382.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027748, A343300, A344030.

Programs

PARI

f(n) = my(fn=factor(n)); sum(k=1, #fn~, fn[k, 1]^k); \\ A343300
lista(nn) = my(p=precprime(nn)); select(x->(x <=p), Set(vector(p, k, f(k)))); \\ Michel Marcus, May 08 2021