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Numbers k such that there exists a number p such that k - p = sopfr(k + p) but no number q exists such that q - k = sopfr(q + k), where sopfr(m) is the sum of the primes dividing m, with repetition.
6

%I #9 Feb 11 2024 09:19:00

%S 7,12,18,20,21,23,27,36,38,42,44,60,64,71,78,88,96,102,104,107,108,

%T 111,126,128,132,133,140,141,142,148,149,152,153,158,174,177,182,183,

%U 192,198,202,204,206,207,211,226,228,234,237,242,244,249,252,258,264,268,282,292,293,308,312,314,318

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

%C These numbers terminate the different series given in A369354.

%H Scott R. Shannon, <a href="/A369357/b369357.txt">Table of n, a(n) for n = 1..10000</a>

%e 21 is a term as 21 - 11 = 10 and sopfr(21 + 11) = sopfr(32) = 10, but no number q exists such that q - 21 = sopfr(q + 21).

%Y Cf. A001414, A369354, A369355, A369356, A369812, A369981, A369348, A369349.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Jan 25 2024