A351866 - OEIS

%I #32 Mar 03 2022 11:46:21

%S 1,14,15,20154,21496,22390,25978,26314,26386,26439,27687,28041,28671,

%T 28911,29365,29397,29559,29607,31135,32263,32335,32665,32669,32785,

%U 33383,33901,34177,34279,34903,35167,35629,35867,36049,36271,36613,36859,205286388,239500772

%N Numbers m such that sigma(m) = tau(m)! where sigma(k) = A000203(k) and tau(k) = A000005(k).

%C Corresponding values of sigma(m): 1, 24, 24, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 40320, ...

%C Corresponding values of tau(m): 1, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, ...

%e sigma(14) = 24 = tau(14)! = 4!.

%t Select[Range[40000], DivisorSigma[1, #] == DivisorSigma[0, #]! &] (* _Amiram Eldar_, Feb 22 2022 *)

%o (Magma) [m: m in [1..5*10^6] | &+Divisors(m) eq Factorial(#Divisors(m))]

%o (PARI) isok(m) = my(f=factor(m)); sigma(f) == numdiv(f)!; \\ _Michel Marcus_, Feb 23 2022

%Y Cf. A000005 (tau), A000203 (sigma), A351865.

%Y Subsequence of A245015.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Feb 22 2022

%E a(37)-a(38) from _Amiram Eldar_, Feb 22 2022