cp's OEIS Frontend

A306655 Numbers n such that lcm(sigma(n), n) = tau(n) * sigma(n) where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).

%I A306655 #30 Sep 08 2022 08:46:21
%S A306655 1,2,18,468,9360,10880,79360,84480,387072,777216,3801600,7282688,
%T A306655 15037440,17418240,27067392,65544192,752903424,1218032640,4227842304,
%U A306655 4737761280,6410638080,11949932544,19327057920,26372530800,37645171200,224956569600,243520929792,876611248128
%N A306655 Numbers n such that lcm(sigma(n), n) = tau(n) * sigma(n) where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).
%C A306655 Numbers n such that A009242(n) = A000005(n) * A000203(n) = A064840(n).
%C A306655 Also numbers n such that A017666(n) = denominator(sigma(n)/n) = tau(n) = A000005(n).
%C A306655 a(29) > 10^12. - _Giovanni Resta_, Mar 04 2019
%e A306655 18 is a term because lcm(sigma(18), 18) = lcm(39, 18) = 234 = tau(18) * sigma(18) = 6 * 39.
%t A306655 Select[Range[1000000], LCM[DivisorSigma[1, #], #] == DivisorSigma[0, #] * DivisorSigma[1, #]&] (* _Vaclav Kotesovec_, Mar 04 2019 *)
%o A306655 (Magma) [n: n in [1..1000000] | LCM(SumOfDivisors(n), n) eq NumberOfDivisors(n)* SumOfDivisors(n)]
%o A306655 (PARI) isok(n) = my(sn = sigma(n)); lcm(sn, n) == sn*numdiv(n); \\ _Michel Marcus_, Mar 04 2019
%Y A306655 Cf. A000005, A000203, A009242, A064840.
%Y A306655 Cf. A069810 (gcd(sigma(n), n) = tau(n)).
%K A306655 nonn
%O A306655 1,2
%A A306655 _Jaroslav Krizek_, Mar 03 2019
%E A306655 a(13)-a(16) from _Vaclav Kotesovec_, Mar 04 2019
%E A306655 a(17) from _Daniel Suteu_, Mar 04 2019
%E A306655 a(18)-a(28) from _Giovanni Resta_, Mar 04 2019