This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A110289 #21 Sep 11 2024 22:52:12
%S A110289 320,432,448,704,720,832,972,1088,1216,1472,1584,1680,1856,1984,2000,
%T A110289 2268,2352,2368,2448,2624,2700,2752,3008,3120,3312,3392,3645,3696,
%U A110289 3776,3904,3920,4176,4212,4288,4368,4400,4544,4672,5056,5103,5200,5312,5488
%N A110289 7-almost primes p*q*r*s*t*u*v relatively prime to p+q+r+s+t+u+v.
%C A110289 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.
%C A110289 Contains p*q^6 if p and q are distinct primes, p >= 5. - _Robert Israel_, Jan 13 2017
%H A110289 Robert Israel, <a href="/A110289/b110289.txt">Table of n, a(n) for n = 1..10000</a>
%e A110289 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.
%p A110289 N:= 10^4: # to get all terms <= N
%p A110289 P:= select(isprime, [$1..N/2^6]):
%p A110289 nP:= nops(P):
%p A110289 Res:= {}:
%p A110289 for p in P do
%p A110289 for q in P while q <= p and p*q*2^5 <= N do
%p A110289 for r in P while r <= q and p*q*r*2^4 <= N do
%p A110289 for s in P while s <= r and p*q*r*s*2^3 <= N do
%p A110289 for t in P while t <= s and p*q*r*s*t*2^2 <= N do
%p A110289 for u in P while u <= t and p*q*r*s*t*u*2 <= N do
%p A110289 for v in P while v <= u and p*q*r*s*t*u*v <= N do
%p A110289 if igcd(p+q+r+s+t+u+v,p*q*r*s*t*u*v) = 1 then
%p A110289 Res:= Res union {p*q*r*s*t*u*v} fi
%p A110289 od od od od od od od:
%p A110289 sort(convert(Res,list)); # _Robert Israel_, Jan 13 2017
%t A110289 Select[Range[6000],PrimeOmega[#]==7&&CoprimeQ[Total[ Times@@@ FactorInteger[ #]],#]&] (* _Harvey P. Dale_, Nov 19 2019 *)
%o A110289 (PARI) sopfr(n)=local(f);if(n<1,0,f=factor(n);sum(k=1,matsize(f)[1],f[k,1]*f[k,2]))
%o A110289 isok(n)=bigomega(n)==7&&gcd(n, sopfr(n))==1 \\ _Rick L. Shepherd_, Jul 20 2005
%Y A110289 Cf. A046308, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110290, A110296, A110297.
%Y A110289 Cf. A001414 (sopfr(n)).
%K A110289 easy,nonn
%O A110289 1,1
%A A110289 _Jonathan Vos Post_, Jul 18 2005
%E A110289 Extended by _Ray Chandler_ and _Rick L. Shepherd_, Jul 20 2005