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A337324
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a(n) is the smallest number m such that gcd(m, tau(m), sigma(m), pod(m)) = n where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
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2
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1, 6, 18, 24, 5000, 90, 66339, 56, 288, 3240, 10036224, 60, 582160384, 20412, 16200, 3968, 49030215219, 612, 4637065216, 1520, 142884, 912384, 98881718827959, 480, 7543125, 479232, 3175200, 5824, 26559758051835904, 76950, 25796647321600, 2688, 491774976, 1268973568
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OFFSET
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1,2
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COMMENTS
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a(35) <= 1289027059712000000.
a(36) <= 136064563937280.
a(37) = 207816012706349056.
a(38) <= 1835772101525504.
a(39) <= 418089296461824.
a(40) <= 11698803719536640.
gcd(m, tau(m), sigma(m), pod(m)) = gcd(m, tau(m), sigma(m)) which may ease the search.
(End)
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LINKS
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EXAMPLE
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For n = 6; a(6) = 90 because 90 is the smallest number with gcd(90, tau(90), sigma(90), pod(90)) = gcd(90, 12, 234, 531441000000) = 6.
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PROG
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(Magma) [Min([m: m in[1..10^5] | GCD([m, #Divisors(m), &+Divisors(m), &*Divisors(m)]) eq k]): k in [1..10]]
(PARI) a(n) = {for(i = 1, oo, f = factor(i); if(gcd([i, numdiv(f), sigma(f)]) == n, return(i)))} \\ David A. Corneth, Aug 24 2020
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CROSSREFS
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Cf. A337323 (gcd(n, tau(n), sigma(n), pod(n))).
Cf. A337325 (least m such that gcd(tau(m), sigma(m), pod(m)) = n).
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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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