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, 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

Links

Table of n, a(n) for n=1..34.

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 A368477

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