A338908 - OEIS

%I #16 Feb 01 2021 22:16:06

%S 10,21,22,34,39,46,55,57,62,82,85,87,91,94,111,115,118,129,133,134,

%T 146,155,159,166,183,187,194,203,205,206,213,218,235,237,247,253,254,

%U 259,267,274,295,298,301,303,314,321,334,335,339,341,358,365,371,377,382

%N Squarefree semiprimes whose prime indices sum to an even number.

%C 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.

%e The sequence of terms together with their prime indices begins:

%e      10: {1,3}     115: {3,9}     213: {2,20}

%e      21: {2,4}     118: {1,17}    218: {1,29}

%e      22: {1,5}     129: {2,14}    235: {3,15}

%e      34: {1,7}     133: {4,8}     237: {2,22}

%e      39: {2,6}     134: {1,19}    247: {6,8}

%e      46: {1,9}     146: {1,21}    253: {5,9}

%e      55: {3,5}     155: {3,11}    254: {1,31}

%e      57: {2,8}     159: {2,16}    259: {4,12}

%e      62: {1,11}    166: {1,23}    267: {2,24}

%e      82: {1,13}    183: {2,18}    274: {1,33}

%e      85: {3,7}     187: {5,7}     295: {3,17}

%e      87: {2,10}    194: {1,25}    298: {1,35}

%e      91: {4,6}     203: {4,10}    301: {4,14}

%e      94: {1,15}    205: {3,13}    303: {2,26}

%e     111: {2,12}    206: {1,27}    314: {1,37}

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

%Y A031215 looks at primes instead of semiprimes.

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

%Y A338905 has this as union of even-indexed rows.

%Y A338906 is the nonsquarefree version.

%Y A338907 is the odd version.

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

%Y A005117 lists squarefree numbers.

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

%Y A024697 is the sum of semiprimes of weight n.

%Y A025129 is the sum of squarefree semiprimes of weight n.

%Y A056239 gives the sum of prime indices of n.

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

%Y A320656 counts factorizations into squarefree semiprimes.

%Y A332765 gives the greatest squarefree semiprime of weight n.

%Y A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.

%Y A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.

%Y A338904 groups semiprimes by weight.

%Y A338911 lists products of pairs of primes both of even index.

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

%Y A339116 groups squarefree semiprimes by greater prime factor.

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Nov 28 2020