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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
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
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).
Sequence in context: A241281 A002744 A320930 * A156382 A214894 A368477
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