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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).
2
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)
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).
Sequence in context: A256266 A228104 A028558 * A140450 A157800 A355228
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