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A096462
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Sum of index values of the prime factors (with multiplicity) of n.
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0
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1, 1, 5, 1, 6, 1, 18, 7, 10, 1, 24, 1, 13, 9, 54, 1, 31, 1, 39, 12, 21, 1, 73, 11, 25, 36, 53, 1, 47, 1, 145, 18, 34, 13, 100, 1, 37, 21, 120, 1, 64, 1, 85, 51, 44, 1, 200, 15, 70, 26, 101, 1, 125, 18, 165, 30, 56, 1, 153, 1, 59, 69, 363, 20, 101, 1, 135, 35, 94, 1, 274, 1, 73, 70
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| Let P be equal to the set of prime factors of the positive integers, counted with multiplicity. Order the members of this set into subsets such that each prime has its own set with an index value assigned to each instance of the prime. Therefore P = {{2_1, 2_2,..2_i}, {3_1, 3_2,..3_j}, . . {p_1, p_2,..p_x}}. In generating the sequence, each indexed instance of a prime can only be used once.
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FORMULA
| a(p)=1 where p is a prime.
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EXAMPLE
| 2 = 2_1, thus a(2)=1
3 = 3_1, thus a(3)=1
4 = 2_2 * 2_3, thus a(4)=5
5 = 5_1, thus a(5)=1
6 = 2_4 * 3_2, thus a(6)=6
7 = 7_1, thus a(7)=1
8 = 2_5 * 2_6 * 2_7, thus a(8)=5+6+7=18, etc.
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MATHEMATICA
| PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; f[n_, p_] := Block[{t = 0, q = p}, While[s = Floor[n/q]; t = t + s; s > 0, q *= p]; t]; g[n_] := Block[{s = 0, pf = PrimeFactors[n], k = 1}, l = Length[pf]; While[k <= l, s = s + Sum[i, {i, f[n - 1, pf[[k]]] + 1, f[n, pf[[k]]]}]; k++ ]; s]; Table[g[n], {n, 2, 75}]
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CROSSREFS
| Cf..
Sequence in context: A176123 A066805 A028284 * A066948 A064265 A180595
Adjacent sequences: A096459 A096460 A096461 * A096463 A096464 A096465
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KEYWORD
| nonn
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AUTHOR
| Andrew Plewe (aplewe(AT)sbcglobal.net), Aug 10 2004
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2004
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