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0, 1, 3, 5, 8, 11, 15, 18, 22, 26, 31, 35, 41, 46, 51, 55, 62, 67, 75, 80, 86, 92, 101, 106, 112, 119, 125, 131, 141, 147, 158, 163, 170, 178, 185, 191, 203, 212, 220, 226, 239, 246, 260, 267, 274, 284, 299, 305, 313, 320, 329, 337, 353, 360, 368, 375, 385, 396, 413
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum(k*e(k)) where k runs through indices of prime factors of n!, while e(k) is the exponent of the corresponding prime factor.
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EXAMPLE
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n=8: 8! = 40320 = 2*2*2*2*2*2*2*3*3*5*7, p-indices = {1,2,3,4}, exponents = {7,2,1,1}; a(8) = 1*7 + 2*2 + 3*1 + 4*1 = 7 + 4 + 3 + 4 = 18.
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MAPLE
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a:= n-> add (numtheory[pi](i[1])*i[2], i=ifactors(n!)[2]):
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MATHEMATICA
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Array[Total[FactorInteger[#!] /. {p_, c_} /; p > 0 :> PrimePi[p] c] &, 59] (* Michael De Vlieger, Jun 26 2020 *)
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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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