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%I #11 Oct 07 2023 11:26:27
%S 1,2,3,5,7,11,13,17,19,23,29,30,31,37,41,42,43,47,53,59,61,66,67,70,
%T 71,73,78,79,83,89,97,101,102,103,105,107,109,110,113,114,127,130,131,
%U 137,138,139,149,151,154,157,163,165,167,170,173,174,179,181,182,186
%N Squarefree non-semiprimes.
%C First differs from A030059 in having 210.
%F Intersection of A005117 and A100959.
%F Complement of A001358 in A005117.
%e The terms together with their prime indices begin:
%e 1: {} 43: {14} 102: {1,2,7}
%e 2: {1} 47: {15} 103: {27}
%e 3: {2} 53: {16} 105: {2,3,4}
%e 5: {3} 59: {17} 107: {28}
%e 7: {4} 61: {18} 109: {29}
%e 11: {5} 66: {1,2,5} 110: {1,3,5}
%e 13: {6} 67: {19} 113: {30}
%e 17: {7} 70: {1,3,4} 114: {1,2,8}
%e 19: {8} 71: {20} 127: {31}
%e 23: {9} 73: {21} 130: {1,3,6}
%e 29: {10} 78: {1,2,6} 131: {32}
%e 30: {1,2,3} 79: {22} 137: {33}
%e 31: {11} 83: {23} 138: {1,2,9}
%e 37: {12} 89: {24} 139: {34}
%e 41: {13} 97: {25} 149: {35}
%e 42: {1,2,4} 101: {26} 151: {36}
%t Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]!=2&]
%o (PARI) isok(k) = my(f=factor(k)); issquarefree(f) && (bigomega(f) != 2); \\ _Michel Marcus_, Oct 07 2023
%Y First condition alone is A005117 (squarefree).
%Y Second condition alone is A100959 (non-semiprime).
%Y The nonprime case is 1 followed by A350352.
%Y Partitions of this type are counted by A365827, non-strict A058984.
%Y A001358 lists semiprimes, squarefree A006881.
%Y Cf. A000009, A004526, A008967, A078408, A365659.
%K nonn
%O 1,2
%A _Gus Wiseman_, Oct 05 2023