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A366744
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The sum of divisors of the least coreful infinitary divisor of n.
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3
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1, 3, 4, 7, 6, 12, 8, 3, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 12, 31, 42, 4, 56, 30, 72, 32, 3, 48, 54, 48, 91, 38, 60, 56, 18, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 12, 72, 24, 80, 90, 60, 168, 62, 96, 104, 7, 84, 144, 68
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OFFSET
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1,2
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COMMENTS
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The number of divisors of the least coreful infinitary divisor of n is A366742(n).
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (p^(A006519(e)+1) - 1)/(p - 1).
Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1 - p/(p^2-1) + Sum_{e>=1} 1/p^f(e)) = 0.696427154..., where f(k) = 2*k - A006519(k) = A339597(k-1).
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MATHEMATICA
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f[p_, e_] := (p^(2^IntegerExponent[e, 2]+1) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
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PROG
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(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(2^valuation(f[i, 2], 2)+1) - 1)/(f[i, 1] -1 )); }
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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