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A326990
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Sum of odd divisors of n that are greater than 1.
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1
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0, 0, 3, 0, 5, 3, 7, 0, 12, 5, 11, 3, 13, 7, 23, 0, 17, 12, 19, 5, 31, 11, 23, 3, 30, 13, 39, 7, 29, 23, 31, 0, 47, 17, 47, 12, 37, 19, 55, 5, 41, 31, 43, 11, 77, 23, 47, 3, 56, 30, 71, 13, 53, 39, 71, 7, 79, 29, 59, 23, 61, 31, 103, 0, 83, 47, 67, 17, 95, 47, 71, 12, 73, 37, 123, 19, 95, 55, 79, 5
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OFFSET
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1,3
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COMMENTS
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Also sum of nonpowers of 2 dividing n, divided the sum of powers of 2 dividing n.
a(n) = 0 iff n is a power of 2.
a(n) = n iff n is an odd prime.
First differs from A284233 at a(15).
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LINKS
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FORMULA
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EXAMPLE
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For n = 18 the divisors of 18 are [1, 2, 3, 6, 9, 18]. The sum of odd divisors of 18 that are greater than 1 is 3 + 9 = 12, so a(18) = 12. On the other hand, there are four divisors of 18 that are not powers of 2, they are [3, 6, 9, 18], and the sum of them is 3 + 6 + 9, 18 = 36. Also there are two divisors of 18 that are powers of 2, they are [1, 2], and the sum of them is 1 + 2 = 3. Then we have that 36/3 = 12, so a(18) = 12.
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PROG
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(Magma) sol:=[]; m:=1; for n in [1..80] do v:=[d:d in Divisors(n)|d gt 1 and IsOdd(d)]; if #v ne 0 then sol[m]:=&+v; m:=m+1; else sol[m]:=0; m:=m+1; end if; end for; sol; // Marius A. Burtea, Aug 24 2019
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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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