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A110289 7-almost primes p*q*r*s*t*u*v relatively prime to p+q+r+s+t+u+v. 12
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

Contains p*q^6 if p and q are distinct primes, p >= 5. - Robert Israel, Jan 13 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

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.

MAPLE

N:= 10^4: # to get all terms <= N

P:= select(isprime, [$1..N/2^6]):

nP:= nops(P):

Res:= {}:

for p in P do

  for q in P while q <= p and p*q*2^5 <= N do

    for r in P while r <= q and p*q*r*2^4 <= N do

      for s in P while s <= r and p*q*r*s*2^3 <= N do

        for t in P while t <= s and p*q*r*s*t*2^2 <= N do

          for u in P while u <= t and p*q*r*s*t*u*2 <= N do

            for v in P while v <= u and p*q*r*s*t*u*v <= N do

              if igcd(p+q+r+s+t+u+v, p*q*r*s*t*u*v) = 1 then

                  Res:= Res union {p*q*r*s*t*u*v} fi

od od od od od od od:

sort(convert(Res, list)); # Robert Israel, Jan 13 2017

PROG

(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, ", "))) \\ Rick L. Shepherd, Jul 20 2005

CROSSREFS

Cf. A046308, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110290, A110296, A110297.

Cf. A001414 (sopfr(n)).

Sequence in context: A064905 A293921 A121010 * A258681 A258674 A237326

Adjacent sequences:  A110286 A110287 A110288 * A110290 A110291 A110292

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jul 18 2005

EXTENSIONS

Extended by Ray Chandler and Rick L. Shepherd, Jul 20 2005

STATUS

approved

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Last modified April 23 02:15 EDT 2019. Contains 322380 sequences. (Running on oeis4.)