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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

(list; graph; refs; listen; history; text; internal format)

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 *)