A365829 Squarefree non-semiprimes.

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30, 31, 37, 41, 42, 43, 47, 53, 59, 61, 66, 67, 70, 71, 73, 78, 79, 83, 89, 97, 101, 102, 103, 105, 107, 109, 110, 113, 114, 127, 130, 131, 137, 138, 139, 149, 151, 154, 157, 163, 165, 167, 170, 173, 174, 179, 181, 182, 186

Offset: 1

Author

Gus Wiseman, Oct 05 2023

Keywords

• nonn

Comments

First differs from A030059 in having 210.

Examples

			The terms together with their prime indices begin:
     1: {}          43: {14}       102: {1,2,7}
     2: {1}         47: {15}       103: {27}
     3: {2}         53: {16}       105: {2,3,4}
     5: {3}         59: {17}       107: {28}
     7: {4}         61: {18}       109: {29}
    11: {5}         66: {1,2,5}    110: {1,3,5}
    13: {6}         67: {19}       113: {30}
    17: {7}         70: {1,3,4}    114: {1,2,8}
    19: {8}         71: {20}       127: {31}
    23: {9}         73: {21}       130: {1,3,6}
    29: {10}        78: {1,2,6}    131: {32}
    30: {1,2,3}     79: {22}       137: {33}
    31: {11}        83: {23}       138: {1,2,9}
    37: {12}        89: {24}       139: {34}
    41: {13}        97: {25}       149: {35}
    42: {1,2,4}    101: {26}       151: {36}
		

Crossrefs

First condition alone is A005117 (squarefree).

Second condition alone is A100959 (non-semiprime).

The nonprime case is 1 followed by A350352.

Partitions of this type are counted by A365827, non-strict A058984.

A001358 lists semiprimes, squarefree A006881.

Cf. A000009, A004526, A008967, A078408, A365659.

Programs

Mathematica

Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]!=2&]

PARI

isok(k) = my(f=factor(k)); issquarefree(f) && (bigomega(f) != 2); \\ Michel Marcus, Oct 07 2023

Formula

Intersection of A005117 and A100959.

Complement of A001358 in A005117.