A351866 Numbers m such that sigma(m) = tau(m)! where sigma(k) = A000203(k) and tau(k) = A000005(k).

1, 14, 15, 20154, 21496, 22390, 25978, 26314, 26386, 26439, 27687, 28041, 28671, 28911, 29365, 29397, 29559, 29607, 31135, 32263, 32335, 32665, 32669, 32785, 33383, 33901, 34177, 34279, 34903, 35167, 35629, 35867, 36049, 36271, 36613, 36859, 205286388, 239500772

Offset: 1

Author

Jaroslav Krizek, Feb 22 2022

Keywords

• nonn
• changed

Comments

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

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

Examples

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

Crossrefs

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

Subsequence of A245015.

Programs

Magma

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

Mathematica

Select[Range[40000], DivisorSigma[1, #] == DivisorSigma[0, #]! &] (* Amiram Eldar, Feb 22 2022 *)

PARI

isok(m) = my(f=factor(m)); sigma(f) == numdiv(f)!; \\ Michel Marcus, Feb 23 2022

Extensions

a(37)-a(38) from Amiram Eldar, Feb 22 2022