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A370504
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.
2
13735, 23, 41205, 46, 3299, 69, 47, 41, 123615, 115, 3859, 107, 2309, 71, 9897, 82, 73, 103, 16165, 71, 141, 253, 2, 119, 943, 119, 26723, 142, 104341, 191, 22009, 89, 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
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
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.
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Feb 20 2024
STATUS
approved