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A260152
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a(n) is the number of distinct sums s + t where s, t are divisors of n.
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1
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1, 3, 3, 6, 3, 9, 3, 10, 6, 10, 3, 16, 3, 10, 9, 15, 3, 19, 3, 20, 10, 10, 3, 26, 6, 10, 10, 20, 3, 28, 3, 21, 10, 10, 10, 33, 3, 10, 10, 32, 3, 32, 3, 21, 18, 10, 3, 40, 6, 21, 10, 21, 3, 33, 10, 32, 10, 10, 3, 50, 3, 10, 20, 28, 10, 33, 3, 21, 10, 34
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OFFSET
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1,2
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COMMENTS
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s and t need not be distinct.
a(n) = 3 if and only if n is prime.
If p is prime, a(p^k) = A000217(k+1).
If p is in A005382, a(p*(2*p-1)) = 9. For all other members of A006881, a(n) = 10.
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LINKS
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EXAMPLE
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For n = 2 the divisors are 1 and 2, and the a(2) = 3 distinct sums are 1+1=2, 1+2=3, 2+2=4.
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MAPLE
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T:= proc(n) local D, x, y;
D:= numtheory:-divisors(n);
nops({seq(seq(x+y, x=D), y=D)})
end proc:
seq(T(n), n=1..100);
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PROG
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(PARI) a(n) = my(v=[], d = divisors(n)); for (i=1, #d, for (j=i, #d, v = concat(v, d[i]+d[j]))); #Set(v); \\ Michel Marcus, Aug 29 2018
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CROSSREFS
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Cf. A048691 (with distinct products s*t rather than sums).
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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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