cp's OEIS Frontend

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).

%I A337325 #28 Sep 08 2022 08:46:25
%S A337325 1,10,18,6,5000,90,66339,30,288,3240,10036224,60,582160384,20412,
%T A337325 16200,168,49030215219,612,4637065216,1520,142884,912384,
%U A337325 98881718827959,420,7543125,479232,14112,5824,26559758051835904,104400,25796647321600,840,491774976,1268973568
%N 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).
%C A337325 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
%e A337325 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.
%o A337325 (Magma) [Min([m: m in[1..10^5] | GCD([#Divisors(m), &+Divisors(m), &*Divisors(m)]) eq k]): k in [1..10]]
%o A337325 (PARI) f(n) = my(d=divisors(factor(n))); gcd([#d, vecsum(d), vecprod(d)]);
%o A337325 a(n) = my(m=1); while (f(m) != n, m++); m; \\ _Michel Marcus_, Sep 21 2020
%Y A337325 Cf. A336722 (gcd(tau(n), sigma(n), pod(n))).
%Y A337325 Cf. A337324 (least m such that gcd(m,tau(m),sigma(m),pod(m)) = n).
%Y A337325 Cf. A000005, A000203, A007955.
%K A337325 nonn
%O A337325 1,2
%A A337325 _Jaroslav Krizek_, Aug 23 2020
%E A337325 a(11) and a(13) from _Amiram Eldar_, Aug 25 2020
%E A337325 More terms from _Jinyuan Wang_, Oct 03 2020