cp's OEIS Frontend

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

%I A338908 #16 Feb 01 2021 22:16:06
%S A338908 10,21,22,34,39,46,55,57,62,82,85,87,91,94,111,115,118,129,133,134,
%T A338908 146,155,159,166,183,187,194,203,205,206,213,218,235,237,247,253,254,
%U A338908 259,267,274,295,298,301,303,314,321,334,335,339,341,358,365,371,377,382
%N A338908 Squarefree semiprimes whose prime indices sum to an even number.
%C A338908 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 A338908 The sequence of terms together with their prime indices begins:
%e A338908      10: {1,3}     115: {3,9}     213: {2,20}
%e A338908      21: {2,4}     118: {1,17}    218: {1,29}
%e A338908      22: {1,5}     129: {2,14}    235: {3,15}
%e A338908      34: {1,7}     133: {4,8}     237: {2,22}
%e A338908      39: {2,6}     134: {1,19}    247: {6,8}
%e A338908      46: {1,9}     146: {1,21}    253: {5,9}
%e A338908      55: {3,5}     155: {3,11}    254: {1,31}
%e A338908      57: {2,8}     159: {2,16}    259: {4,12}
%e A338908      62: {1,11}    166: {1,23}    267: {2,24}
%e A338908      82: {1,13}    183: {2,18}    274: {1,33}
%e A338908      85: {3,7}     187: {5,7}     295: {3,17}
%e A338908      87: {2,10}    194: {1,25}    298: {1,35}
%e A338908      91: {4,6}     203: {4,10}    301: {4,14}
%e A338908      94: {1,15}    205: {3,13}    303: {2,26}
%e A338908     111: {2,12}    206: {1,27}    314: {1,37}
%t A338908 Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&& EvenQ[Total[PrimePi/@First/@FactorInteger[#]]]&]
%Y A338908 A031215 looks at primes instead of semiprimes.
%Y A338908 A300061 and A319241 (squarefree) look all numbers (not just semiprimes).
%Y A338908 A338905 has this as union of even-indexed rows.
%Y A338908 A338906 is the nonsquarefree version.
%Y A338908 A338907 is the odd version.
%Y A338908 A001358 lists semiprimes, with odd/even terms A046315/A100484.
%Y A338908 A005117 lists squarefree numbers.
%Y A338908 A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A338908 A024697 is the sum of semiprimes of weight n.
%Y A338908 A025129 is the sum of squarefree semiprimes of weight n.
%Y A338908 A056239 gives the sum of prime indices of n.
%Y A338908 A289182/A115392 list the positions of odd/even terms in A001358.
%Y A338908 A320656 counts factorizations into squarefree semiprimes.
%Y A338908 A332765 gives the greatest squarefree semiprime of weight n.
%Y A338908 A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A338908 A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A338908 A338904 groups semiprimes by weight.
%Y A338908 A338911 lists products of pairs of primes both of even index.
%Y A338908 A339114/A339115 give the least/greatest semiprime of weight n.
%Y A338908 A339116 groups squarefree semiprimes by greater prime factor.
%Y A338908 Cf. A000040, A001221, A001222, A087112, A098350, A112798, A168472, A338901, A338904, A339004, A339005.
%K A338908 nonn
%O A338908 1,1
%A A338908 _Gus Wiseman_, Nov 28 2020