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Numbers k such that no number p exists such that k - p = sopfr(k + p) and no number q exists such that q - k = sopfr(q + k), where sopfr(m) is the sum of the primes dividing m, with repetition.
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%I #12 Feb 11 2024 09:19:04

%S 2,3,6,8,14,16,22,29,32,33,34,37,39,47,48,50,51,52,54,56,58,59,61,63,

%T 66,69,72,77,81,83,84,85,86,91,93,94,95,97,98,99,103,110,116,117,118,

%U 124,134,135,137,138,139,144,146,147,160,162,164,166,168,171,173,178,179,187,188,189,196,203

%N Numbers k such that no number p exists such that k - p = sopfr(k + p) and no number q exists such that q - k = sopfr(q + k), where sopfr(m) is the sum of the primes dividing m, with repetition.

%H Scott R. Shannon, <a href="/A369356/b369356.txt">Table of n, a(n) for n = 1..10000</a>

%e 22 is a term as there is no number p such that p - 22 = sopfr(p + 22) and there is no number q such that q - 22 = sopfr(q + 22).

%e 4 is not a term as 12 - 4 = 8 and sopfr(12 + 4) = sopfr(16) = 8. Therefore 12 is not a term either.

%Y Cf. A001414, A369354, A369355, A369357, A369812, A369981, A369348, A369349.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Jan 25 2024