A365829 - OEIS

%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