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A110230
5-almost primes p * q * r * s * t not relatively prime to p + q + r + s + t.
12
32, 72, 120, 162, 168, 180, 200, 243, 264, 270, 280, 312, 378, 392, 396, 408, 440, 450, 456, 520, 552, 588, 594, 612, 616, 630, 680, 696, 700, 702, 728, 744, 750, 760, 780, 828, 882, 888, 918, 920, 945, 952, 968, 984, 990, 1026, 1032, 1044, 1050, 1064, 1092
OFFSET
1,1
COMMENTS
p, q, r, s, t are not necessarily distinct. The converse to this is A110229: 5-almost primes p * q * r * s * t which are relatively prime to p+q+r+s+t. A014614 is the 5-almost primes.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
180 is in this sequence because 180 = 2^2 * 3^2 * 5, the sum of the prime factors being 2 + 2 + 3 + 3 + 5 = 15 = 3 * 5 which has two prime factors in common with 180.
PROG
(PARI) list(lim)=my(v=List()); forprime(p=2, lim\16, forprime(q=2, min(p, lim\8\p), my(pq=p*q); forprime(r=2, min(lim\pq\4, q), my(pqr=pq*r); forprime(s=2, min(lim\pqr\2, r), my(pqrs=pqr*s, n); forprime(t=2, min(lim\pqrs, s), n=pqrs*t; if(gcd(n, p+q+r+s+t)>1, listput(v, n))))))); Set(v) \\ Charles R Greathouse IV, Jan 31 2017
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jul 17 2005
EXTENSIONS
Extended by Ray Chandler, Jul 20 2005
STATUS
approved