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%I #27 Jul 06 2020 02:35:35
%S 1152,3200,6272,8748,15488,21632,36992,46208,54675,67712,107163,
%T 107648,123008,175232,215168,236672,264627,282752,312500,359552,
%U 369603,445568,476288,574592,632043,645248,682112,703125,789507,798848,881792,1013888
%N Numbers with prime signature {7,2}, i.e., of form p^7*q^2 with p and q prime.
%H T. D. Noe, <a href="/A179689/b179689.txt">Table of n, a(n) for n = 1..1000</a>
%H OEIS Wiki, <a href="http://oeis.org/wiki/Prime_signature#Numbers_with_same_prime_signature">Numbers with same prime signature</a>.
%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%F Sum_{n>=1} 1/a(n) = P(2)*P(7) - P(9) = A085548 * A085967 - A085969 = 0.001741..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020
%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, 2]
%p do od; k
%p end:
%p seq (a(n), n=1..32); # _Alois P. Heinz_, Jan 23 2011
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,7}; Select[Range[10^6], f]
%o (PARI) list(lim)=my(v=List(),t);forprime(p=2, (lim\4)^(1/7), t=p^7;forprime(q=2, sqrt(lim\t), if(p==q, next);listput(v,t*q^2))); 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.
%Y Cf. A085548, A085967, A085969.
%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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