A277166 Numbers m such that m divides the number of divisors of m!!.

1, 2, 4, 8, 15, 16, 24, 27, 32, 36, 40, 48, 54, 56, 60, 63, 64, 72, 80, 84, 90, 96, 104, 105, 108, 112, 120, 128, 132, 135, 140, 144, 147, 152, 156, 160, 164, 165, 168, 180, 189, 192, 195, 200, 204, 210, 216, 220, 224, 225, 228, 231, 240, 243, 250, 252, 256

Offset: 1

Author

Michel Lagneau, Oct 01 2016

Keywords

• nonn

Comments

It seems that a(n) is asymptotic to c*n with c = 4.8...

Examples

			8 is in the sequence because the number of divisor of 8!! is A114338(8) = 16, which is divisible by 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A006882, A051178, A114338.

Programs

Mathematica

ok[n_] := Divisible[ DivisorSigma[0, n!!], n]; Select[ Range[200], ok]

PARI

isok(n) = (numdiv(prod(i=0, (n-1)\2, n - 2*i)) % n) == 0; \\ after first Pari in A006882; Michel Marcus, Oct 02 2016

Formula

A114338(a(n)) mod a(n) = 0.