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

1,1

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A001221, A055212.

Intersection of A024619 and A137944.

Sequence in context: A260007 A306213 A114819 * A250812 A072413 A131605

Adjacent sequences: A137942 A137943 A137944 * A137946 A137947 A137948

Keyword

nonn

Author

Reinhard Zumkeller, Feb 24 2008

Status

approved