A122181 Numbers n that can be written as n = x*y*z with 1<x<y<z (A122180(n)>0).

24, 30, 36, 40, 42, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 128, 130, 132, 135, 136, 138, 140, 144, 150, 152, 154, 156, 160, 162, 165, 168, 170, 174, 176, 180, 182, 184, 186, 189, 190, 192, 195

Offset

1,1

Comments

Equivalently, numbers n with at least 7 divisors (A000005(n)>6). Equivalently, numbers n with at least 5 proper divisors (A070824(n)>4). Equivalently, numbers n such that i) n has at least three distinct prime factors (A000977), ii) n has two distinct prime factors and four or more total prime factors (n=p^j*q^k, p,q prime, j+k>=4), or iii) n=p^k, a perfect power (A001597) but restricted to prime p and k>=6 [=1+2+3] (some terms of A076470).

Links

Table of n, a(n) for n=1..56.

Example

a(1) = 24 = 2*3*4, a product of three distinct proper divisors (omega(24)=2, bigomega(24)=4).
a(2) = 30 = 2*3*5, a product of three distinct prime factors (omega(30)=3).
a(10) = 64 = 2*4*8 [= 2^1*2^2*2^3] (omega(64)=1, bigomega(64)=6).

Prog

(PARI) for(n=1, 300, if(numdiv(n)>6, print1(n, ", ")) for(n=1, 300, if( (omega(n)==1 && bigomega(n)>5) || (omega(n)==2 && bigomega(n)>3) || (omega(n)>2), print1(n, ", ")))

Crossrefs

Cf. A122179, A122180, A000005, A070824, A000977, A001221, A001222, A001597, A076470.

Sequence in context: A337933 A114635 A077969 * A167758 A248693 A075422

Adjacent sequences: A122178 A122179 A122180 * A122182 A122183 A122184

Keyword

nonn

Author

Rick L. Shepherd, Aug 24 2006

Status

approved