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Search: id:A110290
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| A110290 |
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7-almost primes p*q*r*s*t*u*v not relatively prime to p+q+r+s+t+u+v. |
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12
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| 128, 192, 288, 480, 648, 672, 800, 1008, 1056, 1080, 1120, 1200, 1248, 1458, 1512, 1568, 1620, 1632, 1760, 1800, 1824, 1872, 2080, 2187, 2208, 2376, 2430, 2464, 2520, 2640, 2720, 2736, 2784, 2800, 2808, 2912, 2976, 3000, 3040, 3402, 3528, 3552, 3564
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The primes p, q, r, s, t, u, v are not necessarily distinct. The 7-almost primes are A046308. The converse, A110289, is 7-almost primes p*q*r*s*t*u*v which are relatively prime to p+q+r+s+t+u+v.
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EXAMPLE
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800 = 2^5 * 5^2 is in this sequence because the sum of prime factors 2 + 2 + 2 + 2 + 2 + 5 + 5 = 20 is not relatively prime to 800 (in fact, it is a divisor of 800).
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PROGRAM
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(PARI) sopfr(n)=local(f); if(n<1, 0, f=factor(n); sum(k=1, matsize(f)[1], f[k, 1]*f[k, 2])) for(n=1, 4000, if(bigomega(n)==7&&gcd(n, sopfr(n))>1, print1(n, ", "))) (Shepherd)
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CROSSREFS
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Cf. A046308, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110296, A110297.
Cf. A001414 (sopfr(n)).
Sequence in context: A046307 A036331 A046308 this_sequence A045028 A045053 A114804
Adjacent sequences: A110287 A110288 A110289 this_sequence A110291 A110292 A110293
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Jul 18 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 20 2005
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