A370504 - OEIS

%I #14 Mar 29 2024 08:44:32

%S 13735,23,41205,46,3299,69,47,41,123615,115,3859,107,2309,71,9897,82,

%T 73,103,16165,71,141,253,2,119,943,119,26723,142,104341,191,22009,89,

%U 11577,146,235,151,989,137,6927,142,8,213,659,506,29691,4,7,238,329,119,219,238,3277,199,19295,239,25807

%N The smallest positive number such that sopfr(|a(n) - n|) = sopfr(a(n) + n) and Omega(|a(n) - n|) = Omega(a(n) + n), where sopfr(k) is the sum of the primes dividing k, with repetition.

%C The sequence likely contains all the positive integers, although it takes many terms for some values to appear, e.g., a(41205) = 3. The first value to appear twice is 71 = a(14) = a(20), although numbers which are the product of small primes appear multiple times, e.g., in the first 500000 terms the value 5040 appears 808 times.

%H Scott R. Shannon, <a href="/A370504/b370504.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 13735 as |13735-1| = 13734, 13735+1 = 13736, and soprf(13734) = 124 = soprf(13736), Omega(13734) = 5 = Omega(13736). No smaller number satisfies these requirements.

%e a(2) = 23 as |23-2| = 21, 23+2 = 25, and soprf(21) = 10 = soprf(25), Omega(21) = 2 = Omega(25). No smaller number satisfies these requirements.

%Y Cf. A001414, A001222, A370503, A370502, A369348.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Feb 20 2024