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A064142
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Sum of all distinct primes dividing central binomial coefficient C(n, floor(n/2)).
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1
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0, 2, 3, 5, 7, 7, 12, 14, 12, 12, 23, 23, 29, 29, 32, 34, 48, 48, 62, 62, 61, 61, 81, 81, 73, 73, 69, 69, 98, 98, 127, 129, 123, 123, 130, 130, 148, 148, 161, 161, 195, 195, 227, 227, 204, 204, 251, 251, 253, 253, 257, 257, 307, 307, 323, 323, 316, 316, 367, 367
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OFFSET
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1,2
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LINKS
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FORMULA
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MATHEMATICA
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sop[n_] := If[n<2, 0, Total[First /@ FactorInteger[n]]]; Table[ sop[ Binomial[n, Floor[n/2]]], {n, 60}] (* Giovanni Resta, Jun 22 2018 *)
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PROG
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(PARI) sopf(n)= my(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s)
(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
a(n)=my(s); forprime(p=2, n, my(t=valp(n, p)-valp(n\2, p)-valp(n-n\2, p)); if(t, s+=p)); s \\ Charles R Greathouse IV, Jan 26 2023
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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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