A137945 Non-prime-powers such that the number of composite divisors is a multiple of the number of prime divisors.

36, 100, 120, 144, 168, 196, 225, 264, 270, 280, 312, 324, 378, 400, 408, 440, 441, 456, 484, 520, 552, 576, 594, 616, 676, 680, 696, 702, 728, 744, 750, 760, 784, 888, 918, 920, 945, 952, 960, 984, 1026, 1032, 1064, 1089, 1128, 1144, 1156, 1160, 1225, 1240

Offset: 1

Author

Reinhard Zumkeller, Feb 24 2008

Keywords

• nonn

Examples

			A055212(120) = #{4,6,8,10,12,15,20,24,30,40,60,120} = 12 = 4*A001221(120) = 4*#{2,3,5} = 12, therefore 120 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Reinhard Zumkeller)
• Eric Weisstein's World of Mathematics, Divisor Function

Crossrefs

Cf. A001221, A055212.

Intersection of A024619 and A137944.

Programs

Mathematica

aQ[n_] := (omega = PrimeNu[n]) > 1 && Divisible[DivisorSigma[0, n] - 1, omega]; Select[Range[2, 1240], aQ] (* Amiram Eldar, Aug 31 2019 *)

Formula

A055212(a(n)) mod A001221(a(n)) = 0.