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Numbers k such that there exists a number p such that k - p = sopfr(k) + sopfr(p) but no number q exists such that q - k = sopfr(q) + sopfr(k), where sopfr(m) is the sum of the primes dividing m, with repetition.
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%I #9 Feb 07 2024 09:00:49

%S 16,24,32,36,70,75,81,96,126,128,140,156,174,175,186,190,195,196,198,

%T 200,224,225,242,245,280,288,315,325,340,348,350,351,357,370,385,405,

%U 425,434,442,450,456,472,475,480,481,483,507,510,518,539,544,546,549,550,574,582,595,602,616,620,624

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

%C These numbers terminate the different series given in A369349.

%H Scott R. Shannon, <a href="/A369353/b369353.txt">Table of n, a(n) for n = 1..10000</a>

%e 16 is a term as 16 - 4 = 12 and sopfr(16) + sopfr(4) = 8 + 4 = 12, but no number q exists such that q - 16 = sopfr(q) + sopfr(16).

%Y Cf. A001414, A369348, A369349, A369350, A369351, A369352.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Jan 25 2024