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A338038
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a(n) is the sum of the primes and exponents in the prime factorization of n, but ignoring 1-exponents.
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6
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0, 2, 3, 4, 5, 5, 7, 5, 5, 7, 11, 7, 13, 9, 8, 6, 17, 7, 19, 9, 10, 13, 23, 8, 7, 15, 6, 11, 29, 10, 31, 7, 14, 19, 12, 9, 37, 21, 16, 10, 41, 12, 43, 15, 10, 25, 47, 9, 9, 9, 20, 17, 53, 8, 16, 12, 22, 31, 59, 12, 61, 33, 12, 8, 18, 16, 67, 21, 26, 14, 71, 10
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OFFSET
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1,2
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COMMENTS
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First differs from A106492 for n=64.
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LINKS
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FORMULA
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EXAMPLE
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For n = 18 = 2*3^2, a(18) = 2 + (3+2) = 7.
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MAPLE
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f:= proc(n) local t;
add(t[1]+t[2], t=subs(1=0, ifactors(n)[2]));
end proc:
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MATHEMATICA
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a[1] = 0; a[n_] := Plus @@ First /@ (f = FactorInteger[n]) + Plus @@ Select[Last /@ f, # > 1 &]; Array[a, 100] (* Amiram Eldar, Oct 08 2020 *)
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PROG
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(PARI) a(n) = my(f=factor(n)); vecsum(f[, 1]) + sum(k=1, #f~, if (f[k, 2]!=1, f[k, 2]));
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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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