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%I #23 Jul 17 2019 08:39:11
%S 420,630,660,780,924,990,1020,1050,1092,1140,1170,1380,1386,1428,1470,
%T 1530,1540,1596,1638,1650,1710,1716,1740,1820,1860,1932,1950,2070,
%U 2142,2220,2244,2380,2394,2436,2460,2508,2550,2574,2580,2604,2610,2652,2660,2790
%N Numbers with prime signature (2,1,1,1), i.e., factorization p*q*r*s^2 with distinct primes p, q, r, s.
%C Theorem 4 in Goldston-Graham-Pintz-Yildirim proves that a(n+1) = a(n) + 1 for infinitely many n. - _Charles R Greathouse IV_, Jul 17 2015, corrected by _M. F. Hasler_, Jul 17 2019
%H T. D. Noe, <a href="/A189982/b189982.txt">Table of n, a(n) for n = 1..1000</a>
%H D. A. Goldston, S. W. Graham, J. Pintz, and C. Y. Yıldırım, <a href="http://arxiv.org/abs/0803.2636">Small gaps between almost primes, the parity problem, and some conjectures of Erdos on consecutive integers</a> (2008)
%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,2}; Select[Range[4000],f]
%o (PARI) is(n)=vecsort(factor(n)[,2])==[1, 1, 1, 2]~ \\ _Charles R Greathouse IV_, Jul 17 2015
%Y Part of the list A178739 .. A179696 and A030514 .. A030629, A189975 .. A189990 etc., cf. A101296.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 03 2011
%E Definition reworded by _M. F. Hasler_, Jul 17 2019
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