cp's OEIS Frontend

A365829 Squarefree non-semiprimes.

%I A365829 #11 Oct 07 2023 11:26:27
%S A365829 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 A365829 71,73,78,79,83,89,97,101,102,103,105,107,109,110,113,114,127,130,131,
%U A365829 137,138,139,149,151,154,157,163,165,167,170,173,174,179,181,182,186
%N A365829 Squarefree non-semiprimes.
%C A365829 First differs from A030059 in having 210.
%F A365829 Intersection of A005117 and A100959.
%F A365829 Complement of A001358 in A005117.
%e A365829 The terms together with their prime indices begin:
%e A365829      1: {}          43: {14}       102: {1,2,7}
%e A365829      2: {1}         47: {15}       103: {27}
%e A365829      3: {2}         53: {16}       105: {2,3,4}
%e A365829      5: {3}         59: {17}       107: {28}
%e A365829      7: {4}         61: {18}       109: {29}
%e A365829     11: {5}         66: {1,2,5}    110: {1,3,5}
%e A365829     13: {6}         67: {19}       113: {30}
%e A365829     17: {7}         70: {1,3,4}    114: {1,2,8}
%e A365829     19: {8}         71: {20}       127: {31}
%e A365829     23: {9}         73: {21}       130: {1,3,6}
%e A365829     29: {10}        78: {1,2,6}    131: {32}
%e A365829     30: {1,2,3}     79: {22}       137: {33}
%e A365829     31: {11}        83: {23}       138: {1,2,9}
%e A365829     37: {12}        89: {24}       139: {34}
%e A365829     41: {13}        97: {25}       149: {35}
%e A365829     42: {1,2,4}    101: {26}       151: {36}
%t A365829 Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]!=2&]
%o A365829 (PARI) isok(k) = my(f=factor(k)); issquarefree(f) && (bigomega(f) != 2); \\ _Michel Marcus_, Oct 07 2023
%Y A365829 First condition alone is A005117 (squarefree).
%Y A365829 Second condition alone is A100959 (non-semiprime).
%Y A365829 The nonprime case is 1 followed by A350352.
%Y A365829 Partitions of this type are counted by A365827, non-strict A058984.
%Y A365829 A001358 lists semiprimes, squarefree A006881.
%Y A365829 Cf. A000009, A004526, A008967, A078408, A365659.
%K A365829 nonn
%O A365829 1,2
%A A365829 _Gus Wiseman_, Oct 05 2023