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%I #7 Apr 05 2024 08:21:48
%S 8,32,40,256,264,288,296,512,520,544,552,768,776,800,808,8192,8200,
%T 8224,8232,8448,8456,8480,8488,8704,8712,8736,8744,8960,8968,8992,
%U 9000,16384,16392,16416,16424,16640,16648,16672,16680,16896,16904,16928,16936,17152
%N Numbers whose binary indices are all semiprimes.
%C A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
%e The terms together with their binary expansions and binary indices begin:
%e 8: 1000 ~ {4}
%e 32: 100000 ~ {6}
%e 40: 101000 ~ {4,6}
%e 256: 100000000 ~ {9}
%e 264: 100001000 ~ {4,9}
%e 288: 100100000 ~ {6,9}
%e 296: 100101000 ~ {4,6,9}
%e 512: 1000000000 ~ {10}
%e 520: 1000001000 ~ {4,10}
%e 544: 1000100000 ~ {6,10}
%e 552: 1000101000 ~ {4,6,10}
%e 768: 1100000000 ~ {9,10}
%e 776: 1100001000 ~ {4,9,10}
%e 800: 1100100000 ~ {6,9,10}
%e 808: 1100101000 ~ {4,6,9,10}
%t bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t semi[n_]:=PrimeOmega[n]==2;
%t Select[Range[10000],And@@semi/@bix[#]&]
%Y Partitions of this type are counted by A101048, squarefree case A002100.
%Y For primes instead of semiprimes we get A326782.
%Y For prime indices instead of binary indices we have A339112, A339113.
%Y The squarefree case is A371453.
%Y A001358 lists semiprimes, squarefree A006881.
%Y A005117 lists squarefree numbers.
%Y A048793 lists binary indices, reverse A272020, length A000120, sum A029931.
%Y A070939 gives length of binary expansion.
%Y A096111 gives product of binary indices.
%Y Cf. A087086, A296119, A302478, A326031, A367905, A368109, A368533, A371450.
%K nonn,base
%O 1,1
%A _Gus Wiseman_, Apr 02 2024
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