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A183098
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a(1) = 0, a(n) = sum of divisors d of n such that if d = Product_{i} (p_i^e_i) then not all e_i are > 1.
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5
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0, 2, 3, 2, 5, 11, 7, 2, 3, 17, 11, 23, 13, 23, 23, 2, 17, 29, 19, 37, 31, 35, 23, 47, 5, 41, 3, 51, 29, 71, 31, 2, 47, 53, 47, 41, 37, 59, 55, 77, 41, 95, 43, 79, 68, 71, 47, 95, 7, 67, 71, 93, 53, 83, 71, 107, 79, 89, 59, 163, 61, 95, 94, 2, 83, 143, 67, 121, 95, 143, 71, 65, 73, 113, 98, 135, 95, 167, 79, 157, 3, 125, 83, 219, 107, 131, 119, 167, 89, 224, 111, 163, 127, 143, 119, 191, 97, 121, 146, 87
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OFFSET
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1,2
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COMMENTS
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a(n) = sum of non-powerful divisors d of n where powerful numbers are numbers from A001694(m) for m >= 2.
Sequence is not the same as A183101(n): a(72) = 65, A183101(72) = 137.
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LINKS
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FORMULA
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a(1) = 0, a(p) = p, a(p*q) = p+q+p*q, a(p*q*...*z) = (p+1)*(q+1)*...*(z+1) - 1, a(p^k) = p, for p, q = primes, k = natural numbers, p*q*...*z = product of k (k > 2) distinct primes p, q, ..., z.
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EXAMPLE
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For n = 12, the set of such divisors is {2, 3, 6, 12}; a(12) = 2+3+6+12 = 23.
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MATHEMATICA
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f1[p_, e_] := (p^(e+1)-1)/(p-1); f2[p_, e_] := f1[p, e] - p; a[1] = 0; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) - Times @@ f2 @@@ f; Array[a, 100] (* Amiram Eldar, Aug 29 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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