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A340728
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a(n) is the number of divisors d of n such that n/d - d is prime.
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2
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0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 0, 0, 3, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 0, 1, 1, 0, 2, 0, 1, 0, 3, 0, 2, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 1, 0, 0, 3, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 1
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OFFSET
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1,8
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COMMENTS
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If n is odd, then a(n) = 0 unless n is in A000466, in which case a(n) = 1.
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LINKS
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FORMULA
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EXAMPLE
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a(8) = 2; among the divisors {1,2,4,8} of 8, there are two cases where 8/d-d is prime: 8/1-1 = 7 and 8/2-2 = 2.
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MAPLE
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f:= proc(n) local D, i, m;
D:= sort(convert(numtheory:-divisors(n), list));
m:= nops(D);
nops(select(i -> isprime(D[m+1-i]-D[i]), [$1..(m+1)/2]));
end proc:
map(f, [$1..100]);
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PROG
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(PARI) a(n) = sumdiv(n, d, isprime(n/d-d)); \\ Michel Marcus, Jan 18 2021
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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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