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A306312
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Number of terms of the set of divisors of n that are not the product of any other two distinct divisors.
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0
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1, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 4, 2, 4, 3, 3, 2, 4, 3, 3, 3, 4, 2, 4, 2, 3, 3, 3, 3, 5, 2, 3, 3, 4, 2, 4, 2, 4, 4, 3, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 3, 2, 5, 2, 3, 4, 3, 3, 4, 2, 4, 3, 4, 2, 5, 2, 3, 4, 4, 3, 4, 2, 4, 3, 3, 2, 5, 3, 3, 3, 4
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OFFSET
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1,2
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COMMENTS
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Sets contain 1, primes and powers of primes.
Record values for:
a(1) = 1
a(2) = 2
a(4) = 3
a(12) = 4
a(36) = 5
a(180) = 6
a(900) = 7
a(6300) = 8
a(44100) = 9
a(485100) = 10, ...
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LINKS
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EXAMPLE
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Divisors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198. Here the set is 1, 2, 3, 9, 11 because 2*3 = 6, 2*9 = 18, 2*11 = 22, 3*11 = 33, 6*11 = 66, 9*11 = 99, 2*99 = 198. Then a(198) = 5.
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MAPLE
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with(numtheory): with(combinat): P:=proc(q) local a, b, c, k, n;
for n from 2 to q do if isprime(n) then print(2) else a:=sort([op(divisors(n) minus {1})]); b:=choose(a, 2); c:=[];
for k from 1 to nops(b) do c:=[op(c), b[k][1]*b[k][2]]; od;
a:=[1, op({op(a)} minus {op(c)})]; print(nops(a)); fi; od; end: P(10^6);
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PROG
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(PARI) a(n) = my(f = factor(n)[, 2]); sum(i = 1, #f, min(2, f[i])) \\ David A. Corneth, Feb 06 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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