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Search: id:A110289
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| A110289 |
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7-almost primes p*q*r*s*t*u*v relatively prime to p+q+r+s+t+u+v. |
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12
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| 320, 432, 448, 704, 720, 832, 972, 1088, 1216, 1472, 1584, 1680, 1856, 1984, 2000, 2268, 2352, 2368, 2448, 2624, 2700, 2752, 3008, 3120, 3312, 3392, 3645, 3696, 3776, 3904, 3920, 4176, 4212, 4288, 4368, 4400, 4544, 4672, 5056, 5103, 5200, 5312, 5488
(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, A110290, is 7-almost primes p*q*r*s*t*u*v which are not relatively prime to p+q+r+s+t+u+v.
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EXAMPLE
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832 = 2^6 * 13 is in this sequence because its sum of prime factors is 2 + 2 + 2 + 2 + 2 + 2 + 13 = 25 = 5^2, which has no factor in common with 832.
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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, 7000, 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, A110290, A110296, A110297.
Cf. A001414 (sopfr(n)).
Sequence in context: A053020 A064905 A121010 this_sequence A055863 A045813 A121011
Adjacent sequences: A110286 A110287 A110288 this_sequence A110290 A110291 A110292
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.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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