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 A337325 a(n) is the smallest number m such that gcd(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). 1
 1, 10, 18, 6, 5000, 90, 66339, 30, 288, 3240, 10036224, 60, 582160384, 20412, 16200, 168, 49030215219, 612, 4637065216, 1520, 142884, 912384, 98881718827959, 420, 7543125, 479232, 14112, 5824, 26559758051835904, 104400, 25796647321600, 840, 491774976, 1268973568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS p^(q-1) | a(q). If p != q then (p^(q-1) * q) | a(q) for some primes p and q. A similar idea can be used for nonprime q. - David A. Corneth, Aug 25 2020 LINKS EXAMPLE For n = 6; a(6) = 90 because 90 is the smallest number with gcd(tau(90), sigma(90), pod(90)) = gcd(12, 234, 531441000000) = 6. PROG (MAGMA) [Min([m: m in[1..10^5] | GCD([#Divisors(m), &+Divisors(m), &*Divisors(m)]) eq k]): k in [1..10]] (PARI) f(n) = my(d=divisors(factor(n))); gcd([#d, vecsum(d), vecprod(d)]); a(n) = my(m=1); while (f(m) != n, m++); m; \\ Michel Marcus, Sep 21 2020 CROSSREFS Cf. A336722 (gcd(tau(n), sigma(n), pod(n))). Cf. A337324 (least m such that gcd(m,tau(m),sigma(m),pod(m)) = n). Cf. A000005, A000203, A007955. Sequence in context: A241281 A002744 A320930 * A156382 A214894 A084487 Adjacent sequences:  A337322 A337323 A337324 * A337326 A337327 A337328 KEYWORD nonn AUTHOR Jaroslav Krizek, Aug 23 2020 EXTENSIONS a(11) and a(13) from Amiram Eldar, Aug 25 2020 More terms from Jinyuan Wang, Oct 03 2020 STATUS approved

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Last modified January 25 15:34 EST 2021. Contains 340416 sequences. (Running on oeis4.)