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A036288
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a(n) = 1 + integer log of n: if the prime factorization of n is n = Product (p_j^k_j) then a(n) = 1 + Sum (p_j * k_j) (cf. A001414).
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7
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1, 3, 4, 5, 6, 6, 8, 7, 7, 8, 12, 8, 14, 10, 9, 9, 18, 9, 20, 10, 11, 14, 24, 10, 11, 16, 10, 12, 30, 11, 32, 11, 15, 20, 13, 11, 38, 22, 17, 12, 42, 13, 44, 16, 12, 26, 48, 12, 15, 13, 21, 18, 54, 12, 17, 14, 23, 32, 60, 13, 62, 34, 14, 13, 19, 17, 68, 22
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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Bellamy, O. S.; Cadogan, C. C. Subsets of positive integers: their cardinality and maximality properties. Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), pp. 167--178, Congress. Numer., XXIII-XXIV, Utilitas Math., Winnipeg, Man., 1979. MR0561043 (82b:10006) - From N. J. A. Sloane, May 30 2012
R. Honsberger, Problem 89, Another Curious Sequence, Mathematical Morsels, MAA, 1978, pp. 223-227.
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LINKS
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J. B. Roberts, Problem E2356, Amer. Math. Monthly, 79 (1972); solution by H. Kappus, loc. cit., 80 (1973), p. 810.
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EXAMPLE
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12 = 2^2 * 3 so a(12) = 1 + 2^2 + 3 = 8.
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MAPLE
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f:=proc(n) local i, t1; t1:=ifactors(n)[2]; 1+add( t1[i][1]*t1[i][2], i=1..nops(t1)); end; # N. J. A. Sloane, May 30 2012
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MATHEMATICA
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f[1]=1; f[n_]:=Total[Apply[Times, FactorInteger[n], 1]]+1; f/@Range@68 (* Ivan N. Ianakiev, Apr 18 2016 *)
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PROG
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(Haskell)
a036288 n = 1 + sum (zipWith (*)
(a027748_row n) (map fromIntegral $ a124010_row n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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