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A324554
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a(n) = the smallest number m such that gcd(tau(m), sigma(m)) = n where tau(k) = the number of the divisors of k (A000005) and sigma(k) = the sum of the divisors of k (A000203).
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1
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1, 3, 18, 6, 648, 20, 2916, 30, 288, 304, 82944, 60, 36864, 832, 16200, 168, 5509980288, 612, 31719424, 432, 23328, 44032, 247669456896, 420, 9487368, 258048, 14112, 2496, 31581162962944, 4176, 26843545600, 840, 4064256, 4390912, 42693156, 1980, 151801324109824
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OFFSET
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1,2
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COMMENTS
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a(n) = the smallest number m such that A009205(m) = n.
a(p) = q^(c*p-1) * k for p prime, where q is some prime, c and k are positive integers. - David A. Corneth, Mar 07 2019
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LINKS
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EXAMPLE
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For n=3; a(3) = 18 because gcd(tau(18), sigma(18)) = gcd (6, 39) = 3 and 18 is the smallest.
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MATHEMATICA
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Array[Block[{m = 1}, While[GCD @@ DivisorSigma[{0, 1}, m] != #, m++]; m] &, 16] (* Michael De Vlieger, Mar 24 2019 *)
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PROG
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(Magma) [Min([n: n in[1..10^5] | GCD(NumberOfDivisors(n), SumOfDivisors(n)) eq k]): k in [1..16]]
(PARI) A324554search_and_print(searchlimit) = { my(m = Map(), k); for(n=1, searchlimit, k=gcd(sigma(n), numdiv(n)); if(!mapisdefined(m, k), mapput(m, k, n))); for(k=1, oo, if(!mapisdefined(m, k), break, print1(mapget(m, k), ", "))); }; \\ Antti Karttunen, Mar 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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EXTENSIONS
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STATUS
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approved
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