cp's OEIS Frontend

A339002 Numbers of the form prime(x) * prime(y) where x and y are distinct and have a common divisor > 1.

%I A339002 #14 Nov 27 2020 02:07:25
%S A339002 21,39,57,65,87,91,111,115,129,133,159,183,185,203,213,235,237,247,
%T A339002 259,267,299,301,303,305,319,321,339,365,371,377,393,417,427,445,453,
%U A339002 481,489,497,515,517,519,543,551,553,559,565,579,597,611,623,669,685,687
%N A339002 Numbers of the form prime(x) * prime(y) where x and y are distinct and have a common divisor > 1.
%e A339002 The sequence of terms together with their prime indices begins:
%e A339002      21: {2,4}     235: {3,15}    393: {2,32}
%e A339002      39: {2,6}     237: {2,22}    417: {2,34}
%e A339002      57: {2,8}     247: {6,8}     427: {4,18}
%e A339002      65: {3,6}     259: {4,12}    445: {3,24}
%e A339002      87: {2,10}    267: {2,24}    453: {2,36}
%e A339002      91: {4,6}     299: {6,9}     481: {6,12}
%e A339002     111: {2,12}    301: {4,14}    489: {2,38}
%e A339002     115: {3,9}     303: {2,26}    497: {4,20}
%e A339002     129: {2,14}    305: {3,18}    515: {3,27}
%e A339002     133: {4,8}     319: {5,10}    517: {5,15}
%e A339002     159: {2,16}    321: {2,28}    519: {2,40}
%e A339002     183: {2,18}    339: {2,30}    543: {2,42}
%e A339002     185: {3,12}    365: {3,21}    551: {8,10}
%e A339002     203: {4,10}    371: {4,16}    553: {4,22}
%e A339002     213: {2,20}    377: {6,10}    559: {6,14}
%t A339002 Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&&GCD@@PrimePi/@First/@FactorInteger[#]>1&]
%Y A339002 A300912 is the complement in A001358.
%Y A339002 A338909 is the not necessarily squarefree version.
%Y A339002 A001358 lists semiprimes, with odd and even terms A046315 and A100484.
%Y A339002 A005117 lists squarefree numbers.
%Y A339002 A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A339002 A339005 lists products of pairs of distinct primes of divisible index.
%Y A339002 A320656 counts factorizations into squarefree semiprimes.
%Y A339002 A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A339002 A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A339002 A338910/A338911 list products of pairs of primes both of odd/even index.
%Y A339002 A339003/A339004 list squarefree semiprimes of odd/even index.
%Y A339002 Cf. A001221, A001222, A055684, A056239, A112798, A115392, A166237, A167171, A318990, A320892, A320911, A338901.
%K A339002 nonn
%O A339002 1,1
%A A339002 _Gus Wiseman_, Nov 22 2020