A337324 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).

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

Offset

1,2

Comments

From David A. Corneth, Aug 24 2020: (Start)

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)

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(90, tau(90), sigma(90), pod(90)) = gcd(90, 12, 234, 531441000000) = 6.

Prog

(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

Crossrefs

Cf. A337323 (gcd(n, tau(n), sigma(n), pod(n))).

Cf. A337325 (least m such that gcd(tau(m), sigma(m), pod(m)) = n).

Cf. A000005, A000203, A007955.

Sequence in context: A256266 A228104 A028558 * A140450 A157800 A355228

Adjacent sequences: A337321 A337322 A337323 * A337325 A337326 A337327

Keyword

nonn

Author

Jaroslav Krizek, Aug 23 2020

Extensions

a(11) from Amiram Eldar, Aug 24 2020

More terms from Jaroslav Krizek and David A. Corneth, Aug 24 2020

Status

approved