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%I #22 Jul 19 2017 22:11:55
%S 1920,2688,4224,4480,4992,6528,7040,7296,8320,8832,9856,10880,11136,
%T 11648,11904,12160,14208,14720,15232,15744,16512,17024,18048,18304,
%U 18560,19840,20352,20608,21870,22656,23424,23680,23936,25728,25984,26240,26752,27264
%N Numbers with prime signature {7,1,1}, i.e., of form p^7*q*r with p, q and r prime.
%H T. D. Noe, <a href="/A179696/b179696.txt">Table of n, a(n) for n = 1..1000</a>
%H Will Nicholes <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%H OEIS Wiki, <a href="http://oeis.org/wiki/Prime_signature#Numbers_with_same_prime_signature">Numbers with same prime signature</a>.
%p a:= proc(n) option remember; local k;
%p for k from 1+ `if` (n=1, 1, a(n-1))
%p while sort (map (x-> x[2], ifactors(k)[2]), `>`)<>[7, 1, 1]
%p do od; k
%p end:
%p seq (a(n), n=1..40); # _Alois P. Heinz_, Jan 23 2011
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,7}; Select[Range[30000], f]
%o (PARI) list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\6)^(1/7), t1=p^7;forprime(q=2, lim\t1, if(p==q, next);t2=t1*q;forprime(r=q+1, lim\t2, if(p==r,next);listput(v,t2*r)))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011
%Y Cf. A006881, A007304, A065036, A085986, A085987, A092759, A178739, A179642, A179643, A179644, A179645, A179646, A179664, A179665, A179666, A179667, A179668, A179669, A179670, A179671, A179672, A179688, A179689, A179690, A179691, A179692, A179693, A179694, A179695.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 24 2010
%E Title edited by _Daniel Forgues_, Jan 22 2011
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