cp's OEIS Frontend

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

%I A344023 #50 May 09 2021 08:20:01
%S A344023 0,2,3,5,7,11,13,17,19,23,27,28,29,31,37,41,43,47,51,52,53,54,59,61,
%T A344023 67,71,73,79,83,89,97,101,103,107,109,113,123,124,126,127,128,131,136,
%U A344023 137,139,149,151,157,163,167,171,172,173,174,176,179,180,181,191,193,197,199
%N A344023 Numbers of the form p_1^1 + p_2^2 + ... + p_k^k where p_1 < p_2 < ... < p_k are distinct primes.
%C A344023 Also, ordered distinct values taken by terms of A343300.
%C A344023 Primes form the subsequence corresponding to k = 1.
%H A344023 David A. Corneth, <a href="/A344023/b344023.txt">Table of n, a(n) for n = 1..10000</a>
%e A344023 0 is a term  because it is the empty sum.
%e A344023 11 is a term because 11 = 11^1 is prime and also 11 = 2^1 + 3^2.
%e A344023 52 is a term because 3^1 + 7^2 = 52.
%e A344023 1382 is a term because 2^1 + 7^2 + 11^3 = 13^1 +37^2 = 1382.
%o A344023 (PARI) f(n) = my(fn=factor(n)); sum(k=1, #fn~, fn[k, 1]^k); \\ A343300
%o A344023 lista(nn) = my(p=precprime(nn)); select(x->(x <=p), Set(vector(p, k, f(k)))); \\ _Michel Marcus_, May 08 2021
%Y A344023 Cf. A027748, A343300, A344030.
%K A344023 nonn
%O A344023 1,2
%A A344023 _Bernard Schott_, May 07 2021