A338908 Squarefree semiprimes whose prime indices sum to an even number.

10, 21, 22, 34, 39, 46, 55, 57, 62, 82, 85, 87, 91, 94, 111, 115, 118, 129, 133, 134, 146, 155, 159, 166, 183, 187, 194, 203, 205, 206, 213, 218, 235, 237, 247, 253, 254, 259, 267, 274, 295, 298, 301, 303, 314, 321, 334, 335, 339, 341, 358, 365, 371, 377, 382

Offset: 1

Author

Gus Wiseman, Nov 28 2020

Keywords

• nonn

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.

Examples

			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}
		

Crossrefs

A031215 looks at primes instead of semiprimes.

A300061 and A319241 (squarefree) look all numbers (not just semiprimes).

A338905 has this as union of even-indexed rows.

A338906 is the nonsquarefree version.

A338907 is the odd version.

A001358 lists semiprimes, with odd/even terms A046315/A100484.

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.

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.

A289182/A115392 list the positions of odd/even terms in A001358.

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.

A339114/A339115 give the least/greatest semiprime of weight n.

A339116 groups squarefree semiprimes by greater prime factor.

Cf. A000040, A001221, A001222, A087112, A098350, A112798, A168472, A338901, A338904, A339004, A339005.

Programs

Mathematica

Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&& EvenQ[Total[PrimePi/@First/@FactorInteger[#]]]&]