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Revision History for A110297

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A110297

8-almost primes p*q*r*s*t*u*v*w not relatively prime to p+q+r+s+t+u+v+w.
(history; published version)

#9 by Charles R Greathouse IV at Wed Feb 01 09:09:15 EST 2017

STATUS

editing

approved

#8 by Charles R Greathouse IV at Wed Feb 01 09:09:13 EST 2017

LINKS

Charles R Greathouse IV, <a href="/A110297/b110297.txt">Table of n, a(n) for n = 1..10000</a>

PROG

(PARI) list(lim)=my(v=List()); forprime(p=2, lim\128, forprime(q=2, min(p, lim\64\p), my(pq=p*q); forprime(r=2, min(lim\pq\32, q), my(pqr=pq*r); forprime(s=2, min(lim\pqr\16, r), my(pqrs=pqr*s); forprime(t=2, min(lim\pqrs\8, s), my(pqrst=pqrs*t); forprime(u=2, min(lim\pqrst\4, t), my(pqrstu=pqrst*u); forprime(w=2, min(lim\pqrstu\2, u), my(pqrstuw=pqrstu*w, n); forprime(x=2, min(lim\pqrstuw, w), n=pqrstuw*x; if(gcd(n, p+q+r+s+t+u+w+x)>1, listput(v, n)))))))))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

STATUS

approved

editing

#7 by Russ Cox at Fri Mar 30 18:40:29 EDT 2012

AUTHOR

_Jonathan Vos Post (jvospost3(AT)gmail.com), _, Jul 18 2005

Discussion

Fri Mar 30

18:40

OEIS Server: https://oeis.org/edit/global/228

#6 by Russ Cox at Fri Mar 30 17:29:49 EDT 2012

EXTENSIONS

Extended by _Ray Chandler (rayjchandler(AT)sbcglobal.net), _, Jul 20 2005

Discussion

Fri Mar 30

17:29

OEIS Server: https://oeis.org/edit/global/154

#5 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

EXAMPLE

576 = 2^6 * 3^2 is an element of this sequence because its sum of prime factors is 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 = 18 = 2 * 3^2 which is a factor of 576, and not relatively prime to 576.

KEYWORD

easy,nonn,new

#4 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

easy,nonn,new

AUTHOR

Jonathan Vos Post (jvospost2jvospost3(AT)yahoogmail.com), Jul 18 2005

#3 by N. J. A. Sloane at Fri Jan 12 03:00:00 EST 2007

KEYWORD

easy,nonn,new

EXTENSIONS

Extended by Ray Chandler (RayChandlerrayjchandler(AT)alumni.tcusbcglobal.edunet), Jul 20 2005

#2 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

DATA

256, 576, 896, 960, 1296, 1344, 1440, 1600, 1944, 2112, 2160, 2240, 2496, 2916, 3024, 3136, 3168, 3264, 3360, 3520, 3600, 3648, 4000, 4160, 4416, 4704, 4752, 4860, 4896, 4928, 5040, 5400, 5440, 5568, 5616, 5824, 5952, 6000, 6080, 6561, 6624, 6804, 7056

CROSSREFS

Cf. A046308, A046310, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110290, A110296.

KEYWORD

easy,nonn,new

EXTENSIONS

Extended by Ray Chandler (RayChandler(AT)alumni.tcu.edu), Jul 20 2005

#1 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

NAME

8-almost primes p*q*r*s*t*u*v*w not relatively prime to p+q+r+s+t+u+v+w.

DATA

256, 576, 896, 960, 1296, 1344, 1440, 1600, 1944, 2112, 2160, 2240, 2496, 2916, 3024, 3136, 3168, 3264, 3360, 3520, 3600, 3648, 4000, 4160, 4416, 4704

OFFSET

1,1

COMMENTS

The primes p, q, r, s, t, u, v, w are not necessarily distinct. The 8-almost primes are A046310. The converse, A110296, is 8-almost primes p*q*r*s*t*u*v*w which are relatively prime to p+q+r+s+t+u+v+w.

EXAMPLE

576 = 2^6 * 3^2 is an element of this sequence because its sum of prime factors is 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 = 18 = 2 * 3^2 which is a factor of 576, and not relatively prime to 576.

CROSSREFS

Cf. A046308, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110290, A110296.

KEYWORD

easy,nonn,new

AUTHOR

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jul 18 2005

STATUS

approved