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A308135
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Sum of non-coreful divisors of n.
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7
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0, 1, 1, 1, 1, 6, 1, 1, 1, 8, 1, 10, 1, 10, 9, 1, 1, 15, 1, 12, 11, 14, 1, 18, 1, 16, 1, 14, 1, 42, 1, 1, 15, 20, 13, 19, 1, 22, 17, 20, 1, 54, 1, 18, 18, 26, 1, 34, 1, 33, 21, 20, 1, 42, 17, 22, 23, 32, 1, 78, 1, 34, 20, 1, 19, 78, 1, 24, 27, 74, 1, 27, 1, 40
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OFFSET
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1,6
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COMMENTS
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Non-coreful divisor d of a number k is a divisor such that rad(d) != rad(k), where rad(k) is the largest squarefree divisor of k (A007947).
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LINKS
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G. E. Hardy and M. V. Subbarao, Highly powerful numbers, Congress. Numer., Vol. 37 (1983), pp. 277-307. (Annotated scanned copy)
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FORMULA
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EXAMPLE
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a(15) = 9. Prime factors of 15 are 3, 5 and its divisors are 1, 3, 5, 15. The non-coreful divisors are 1, 3, 5 and their sum is 9.
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MAPLE
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with(numtheory): P:=proc(k) local a, n; a:=mul(n, n=factorset(k));
sigma(k)-a*sigma(k/a); end: seq(P(i), i=1..74);
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MATHEMATICA
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f[p_, e_] := (p^(e + 1) - 1)/(p - 1); fc[p_, e_] := f[p, e] - 1; a[1] = 0; a[n_] := Times @@ (f @@@ FactorInteger[n]) - Times @@ (fc @@@ FactorInteger[n]); Array[a, 100]
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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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