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A180868 Numbers n such that n and n+1 are semiprime powers.

%I A180868 #17 Nov 21 2020 16:23:27
%S A180868 9,14,15,21,25,33,34,35,38,57,64,81,85,86,93,94,118,121,122,133,141,
%T A180868 142,145,158,177,201,202,205,213,214,215,216,217,218,225,253,298,301,
%U A180868 302,326,334,361,381,393,394,445,446,453,481,484,501
%N A180868 Numbers n such that n and n+1 are semiprime powers.
%C A180868 This is to semiprimes A001358 and powers of semiprimes A085155 as A006549 is to primes A000040 and powers of primes A000961.
%H A180868 Alois P. Heinz, <a href="/A180868/b180868.txt">Table of n, a(n) for n = 1..1000</a>
%F A180868 { n : {n,n+1} is subset of {A085155} } = { n : n = A001358(i)^j and n+1 = A001358(k)^m }.
%e A180868 15 is in the sequence because 15 = (3*5)^1 and 15+1 = 16 = (2*2)^2 are both semiprime powers.
%p A180868 spp:= proc(n) option remember; local l;
%p A180868         if n<2 or isprime(n) then false
%p A180868         else l:= ifactors(n)[2];
%p A180868              if nops(l)>2 then false
%p A180868            elif nops(l)=2 then evalb(l[1][2]=l[2][2])
%p A180868            else evalb(irem(l[1][2], 2)=0)
%p A180868              fi
%p A180868         fi
%p A180868       end:
%p A180868 a:= proc(n) option remember; local k;
%p A180868       for k from 1+ `if`(n=1, 8, a(n-1))
%p A180868         while not spp(k) or not spp(k+1)
%p A180868       do od; k
%p A180868     end:
%p A180868 seq(a(n), n=1..80);  # _Alois P. Heinz_, Jan 22 2011
%t A180868 sppQ[n_] := With[{f = FactorInteger[n][[All, 2]]}, n==1 || Length[f]==1 && EvenQ[f[[1]]] || Length[f]==2 && f[[1]]==f[[2]]];
%t A180868 Select[Range[1000], sppQ[#] && sppQ[#+1]&] (* _Jean-François Alcover_, Nov 21 2020 *)
%Y A180868 Cf. A000961, A001358, A006549, A085155.
%K A180868 nonn,easy
%O A180868 1,1
%A A180868 _Jonathan Vos Post_, Jan 22 2011
%E A180868 More terms and edited by _Alois P. Heinz_, Jan 22 2011