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A344023
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Numbers of the form p_1^1 + p_2^2 + ... + p_k^k where p_1 < p_2 < ... < p_k are distinct primes.
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2
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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
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OFFSET
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1,2
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COMMENTS
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Also, ordered distinct values taken by terms of A343300.
Primes form the subsequence corresponding to k = 1.
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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