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A240591
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The smaller of a pair of successive powerful numbers (A001694) without any prime number between them.
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3
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8, 25, 32, 121, 288, 675, 1331, 1369, 1936, 2187, 2700, 3125, 5324, 6724, 9800, 10800, 12167, 15125, 32761, 39200, 48668, 70225, 79507, 88200, 97336, 107648, 143641, 156800, 212521, 228484, 235224, 280900, 312481, 332928, 456968, 465124, 574564, 674028, 744769, 829921, 830297, 857476, 877952, 940896
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OFFSET
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1,1
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LINKS
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EXAMPLE
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25 is in the sequence because A001694(6)=25, A001694(7)=27, without primes between them.
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MATHEMATICA
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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 *)
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PROG
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(PARI)
ispowerful(n)={local(h); if(n==1, h=1, h=(vecmin(factor(n)[, 2])>1)); return(h)}
nextpowerful(n)={local(k); k=n+1; while(!ispowerful(k), k+=1); return(k)}
{for(i=1, 10^6, if(ispowerful(i), if(nextprime(i)>=nextpowerful(i), print1(i, ", "))))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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