OFFSET
1,2
COMMENTS
A squarefree semiprime is a product of any two distinct prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.
EXAMPLE
The sequence of terms together with their prime indices begins:
6: {1,2} 57: {2,8} 106: {1,16} 155: {3,11}
10: {1,3} 58: {1,10} 111: {2,12} 158: {1,22}
14: {1,4} 62: {1,11} 115: {3,9} 159: {2,16}
15: {2,3} 65: {3,6} 118: {1,17} 161: {4,9}
21: {2,4} 69: {2,9} 119: {4,7} 166: {1,23}
22: {1,5} 74: {1,12} 122: {1,18} 177: {2,17}
26: {1,6} 77: {4,5} 123: {2,13} 178: {1,24}
33: {2,5} 82: {1,13} 129: {2,14} 183: {2,18}
34: {1,7} 85: {3,7} 133: {4,8} 185: {3,12}
35: {3,4} 86: {1,14} 134: {1,19} 187: {5,7}
38: {1,8} 87: {2,10} 141: {2,15} 194: {1,25}
39: {2,6} 91: {4,6} 142: {1,20} 201: {2,19}
46: {1,9} 93: {2,11} 143: {5,6} 202: {1,26}
51: {2,7} 94: {1,15} 145: {3,10} 203: {4,10}
55: {3,5} 95: {3,8} 146: {1,21} 205: {3,13}
MATHEMATICA
Join@@Cases[Select[Range[100], SquareFreeQ[#]&&PrimeOmega[#]==2&], k_:>PrimePi/@First/@FactorInteger[k]]
CROSSREFS
A270650 is the first column.
A270652 is the second column.
A320656 counts multiset partitions using these rows, or factorizations into squarefree semiprimes.
A338900 gives row differences.
A338901 gives the row numbers for first appearances.
A001358 lists semiprimes.
A004526 counts 2-part partitions, with strict case shifted right once.
A005117 lists squarefree numbers.
A006881 lists squarefree semiprimes.
A046388 lists odd squarefree semiprimes.
A166237 gives first differences of squarefree semiprimes.
KEYWORD
AUTHOR
Gus Wiseman, Nov 16 2020
STATUS
approved