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0, 2, 5, 3, 8, 5, 12, 12, 12, 7, 18, 18, 31, 24, 24, 24, 41, 41, 60, 60, 60, 49, 72, 72, 72, 59, 59, 59, 88, 88, 119, 119, 119, 102, 102, 102, 139, 120, 120, 120, 161, 161, 204, 204, 204, 181, 228, 228, 228, 228, 228, 228, 281, 281, 281, 281, 281, 252, 311, 311
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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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a(n) = Sum_{k=floor(n/2)+1..n} k*c(k), where c is the prime characteristic (A010051). - Wesley Ivan Hurt, Dec 23 2023
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EXAMPLE
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Prime factors in 20! which have exponent=1 (i.e., unitary p-divisors) are {11,13,17,19}; sum = 60, so a(20)=60. (The sum of all its prime factors (unitary and non-unitary) is A034387(20).)
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MAPLE
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a:= n-> add(`if`(i[2]=1, i[1], 0), i=ifactors(n!)[2]):
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MATHEMATICA
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a[n_] := Select[FactorInteger[n!], #[[2]] == 1&][[All, 1]] // Total;
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PROG
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(PARI) a(n) = my(f=factor(n!)~); sum(i=1, length(f), if (f[2, i]==1, f[1, i])); \\ Harry J. Smith, Sep 04 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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