OFFSET
1,1
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:
10: {1,3} 115: {3,9} 213: {2,20}
21: {2,4} 118: {1,17} 218: {1,29}
22: {1,5} 129: {2,14} 235: {3,15}
34: {1,7} 133: {4,8} 237: {2,22}
39: {2,6} 134: {1,19} 247: {6,8}
46: {1,9} 146: {1,21} 253: {5,9}
55: {3,5} 155: {3,11} 254: {1,31}
57: {2,8} 159: {2,16} 259: {4,12}
62: {1,11} 166: {1,23} 267: {2,24}
82: {1,13} 183: {2,18} 274: {1,33}
85: {3,7} 187: {5,7} 295: {3,17}
87: {2,10} 194: {1,25} 298: {1,35}
91: {4,6} 203: {4,10} 301: {4,14}
94: {1,15} 205: {3,13} 303: {2,26}
111: {2,12} 206: {1,27} 314: {1,37}
MATHEMATICA
Select[Range[100], SquareFreeQ[#]&&PrimeOmega[#]==2&& EvenQ[Total[PrimePi/@First/@FactorInteger[#]]]&]
CROSSREFS
A031215 looks at primes instead of semiprimes.
A338905 has this as union of even-indexed rows.
A338906 is the nonsquarefree version.
A338907 is the odd version.
A005117 lists squarefree numbers.
A024697 is the sum of semiprimes of weight n.
A025129 is the sum of squarefree semiprimes of weight n.
A056239 gives the sum of prime indices of n.
A320656 counts factorizations into squarefree semiprimes.
A332765 gives the greatest squarefree semiprime of weight n.
A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.
A338904 groups semiprimes by weight.
A338911 lists products of pairs of primes both of even index.
A339116 groups squarefree semiprimes by greater prime factor.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 28 2020
STATUS
approved