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A361174
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The sum of the exponential squarefree exponential divisors (or e-squarefree e-divisors) of n.
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2
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1, 2, 3, 6, 5, 6, 7, 10, 12, 10, 11, 18, 13, 14, 15, 6, 17, 24, 19, 30, 21, 22, 23, 30, 30, 26, 30, 42, 29, 30, 31, 34, 33, 34, 35, 72, 37, 38, 39, 50, 41, 42, 43, 66, 60, 46, 47, 18, 56, 60, 51, 78, 53, 60, 55, 70, 57, 58, 59, 90, 61, 62, 84, 78, 65, 66, 67, 102
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OFFSET
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1,2
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COMMENTS
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The exponential squarefree exponential divisors (or e-squarefree e-divisors) of n = Product_i p(i)^e(i) are all the numbers of the form Product_i p(i)^d(i) where d(i) is a squarefree divisor of e(i).
The number of exponential squarefree exponential divisors of n is A278908(n).
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LINKS
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FORMULA
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Multiplicative with a(p^e) = Sum_{d|e, d squarefree} p^d.
Sum_{k=1..n} a(k) ~ c * n^2 / 2, c = Product_{p prime} (1 + Sum_{k>=2} (a(p^k) - p*a(p^(k-1)))/p^(2*k)) = 1.08989220899432387559... . - Amiram Eldar, Feb 13 2024
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MATHEMATICA
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f[p_, e_] := DivisorSum[e, p^# &, SquareFreeQ[#] &]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
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PROG
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(PARI) ff(p, e) = sumdiv(e, d, if(issquarefree(d), p^d, 0));
a(n) = {my(f=factor(n)); prod(i=1, #f~, ff(f[i, 1], f[i, 2])); }
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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