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5-almost primes p * q * r * s * t relatively prime to p + q + r + s + t.
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%I #10 Jan 31 2017 16:53:26

%S 48,80,108,112,176,208,252,272,300,304,368,405,420,464,468,496,500,

%T 567,592,656,660,675,684,688,752,848,891,924,944,976,980,1020,1053,

%U 1072,1116,1136,1140,1168,1264,1300,1323,1328,1332,1372,1377,1424,1428,1452

%N 5-almost primes p * q * r * s * t relatively prime to p + q + r + s + t.

%C p, q, r, s, t are not necessarily distinct. The converse to this is A110230: 5-almost primes p * q * r * s * t which are not relatively prime to p+q+r+s+t. A014614 is the 5-almost primes.

%H Charles R Greathouse IV, <a href="/A110229/b110229.txt">Table of n, a(n) for n = 1..10000</a>

%e 48 is in this sequence because 48 = 2^4 * 3, which has no factors in common with 2 + 2 + 2 + 2 + 3 = 11.

%o (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

%Y Cf. A014614, A002033, A110187, A110188, A110227, A110228, A110230, A110231, A110232, A110289, A110290, A110296, A110297.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jul 17 2005

%E Extended by _Ray Chandler_, Jul 20 2005

%E Incorrect formula and comment of Sep 2009 related to A002033 deleted - _R. J. Mathar_, Oct 14 2009