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A088948
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Numbers k such that (A006530(k) + A020639(k))/2 is an integer; that is, arithmetic mean of least and largest prime factor is an integer.
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3
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2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125
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OFFSET
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1,1
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COMMENTS
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Union of odd numbers and powers of 2 minus {1}. - Ivan Neretin, Dec 30 2015
In other words, the symmetric difference of sets A005408 (all prime factors are odd) and A000079 (all prime factors are even). If we had allowed 1 as a member, it would have been the union of A005408 and A000079, as stated. - Jeppe Stig Nielsen, Dec 27 2019
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LINKS
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EXAMPLE
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Primes and prime powers are here.
Also other composites: n=105, (3+7)/2 = 5 is an integer (and, moreover, divides n).
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MATHEMATICA
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Rest@ Select[Range@ 125, IntegerQ[(FactorInteger[#][[1, 1]] + FactorInteger[#][[-1, 1]])/2] &] (* Michael De Vlieger, Mar 28 2015 *)
amintQ[n_]:=Module[{fi=FactorInteger[n][[;; , 1]]}, IntegerQ[Mean[{fi[[1]], fi[[-1]]}]]]; Select[Range[150], amintQ] (* Harvey P. Dale, Mar 02 2023 *)
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PROG
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(PARI) is_a088948(n) = {local (f); f=factor(n); if(Mod(vecmin(f[, 1])+vecmax(f[, 1]), 2)==0, 1, 0)} \\ Michael B. Porter, Mar 28 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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