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%I #19 Jan 30 2023 02:38:59
%S 8,25,32,121,288,675,1331,1369,1936,2187,2700,3125,5324,6724,9800,
%T 10800,12167,15125,32761,39200,48668,70225,79507,88200,97336,107648,
%U 143641,156800,212521,228484,235224,280900,312481,332928,456968,465124,574564,674028,744769,829921,830297,857476,877952,940896
%N The smaller of a pair of successive powerful numbers (A001694) without any prime number between them.
%H Amiram Eldar, <a href="/A240591/b240591.txt">Table of n, a(n) for n = 1..103</a> (terms below 10^9)
%e 25 is in the sequence because A001694(6)=25, A001694(7)=27, without primes between them.
%t Select[Partition[Join[{1},Select[Range[10^6],Min@FactorInteger[#][[All, 2]]> 1&]],2,1],PrimePi[#[[1]]]==PrimePi[#[[2]]]&][[All,1]] (* _Harvey P. Dale_, Mar 28 2018 *)
%o (PARI)
%o ispowerful(n)={local(h);if(n==1,h=1,h=(vecmin(factor(n)[, 2])>1));return(h)}
%o nextpowerful(n)={local(k);k=n+1;while(!ispowerful(k),k+=1);return(k)}
%o {for(i=1,10^6,if(ispowerful(i),if(nextprime(i)>=nextpowerful(i),print1(i, ", "))))}
%Y Supersequence of A060355.
%Y Cf. A001694, A240590.
%K nonn
%O 1,1
%A _Antonio Roldán_, Apr 08 2014
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