A339003 - OEIS

%I #11 Jan 06 2021 16:18:31

%S 10,22,34,46,55,62,82,85,94,115,118,134,146,155,166,187,194,205,206,

%T 218,235,253,254,274,295,298,314,334,335,341,358,365,382,391,394,415,

%U 422,451,454,466,482,485,514,515,517,527,538,545,554,566,614,626,635,649

%N Numbers of the form prime(x) * prime(y) where x and y are distinct and both odd.

%C The squarefree semiprimes in A332822. - _Peter Munn_, Dec 25 2020

%F Numbers m such that A001221(m) = A001222(m) = A195017(m) = 2. - _Peter Munn_, Dec 31 2020

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

%e      10: {1,3}     187: {5,7}     358: {1,41}    527: {7,11}

%e      22: {1,5}     194: {1,25}    365: {3,21}    538: {1,57}

%e      34: {1,7}     205: {3,13}    382: {1,43}    545: {3,29}

%e      46: {1,9}     206: {1,27}    391: {7,9}     554: {1,59}

%e      55: {3,5}     218: {1,29}    394: {1,45}    566: {1,61}

%e      62: {1,11}    235: {3,15}    415: {3,23}    614: {1,63}

%e      82: {1,13}    253: {5,9}     422: {1,47}    626: {1,65}

%e      85: {3,7}     254: {1,31}    451: {5,13}    635: {3,31}

%e      94: {1,15}    274: {1,33}    454: {1,49}    649: {5,17}

%e     115: {3,9}     295: {3,17}    466: {1,51}    662: {1,67}

%e     118: {1,17}    298: {1,35}    482: {1,53}    685: {3,33}

%e     134: {1,19}    314: {1,37}    485: {3,25}    694: {1,69}

%e     146: {1,21}    334: {1,39}    514: {1,55}    697: {7,13}

%e     155: {3,11}    335: {3,19}    515: {3,27}    706: {1,71}

%e     166: {1,23}    341: {5,11}    517: {5,15}    713: {9,11}

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

%Y A338910 is the not necessarily squarefree version.

%Y A339004 is the even instead of odd version.

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

%Y A005117 lists squarefree numbers.

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

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

%Y A300912 lists products of two primes of relatively prime index.

%Y A320656 counts factorizations into squarefree semiprimes.

%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 A338906/A338907 list semiprimes of even/odd weight.

%Y A339002 lists products of two distinct primes of non-relatively prime index.

%Y A339005 lists products of two distinct primes of divisible index.

%Y Cf. A001221, A001222, A056239, A112798, A166237, A195017, A318990, A320911, A338901, A338903, A338911.

%Y Subsequence of A332822.

%K nonn

%O 1,1

%A _Gus Wiseman_, Nov 21 2020