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

1,2

Comments

Also, ordered distinct values taken by terms of A343300.

Primes form the subsequence corresponding to k = 1.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A027748, A343300, A344030.

Sequence in context: A257691 A372059 A164574 * A079603 A095959 A359802

Adjacent sequences: A344020 A344021 A344022 * A344024 A344025 A344026

Keyword

nonn

Author

Bernard Schott, May 07 2021

Status

approved