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

21, 39, 57, 65, 87, 91, 111, 115, 129, 133, 159, 183, 185, 203, 213, 235, 237, 247, 259, 267, 299, 301, 303, 305, 319, 321, 339, 365, 371, 377, 393, 417, 427, 445, 453, 481, 489, 497, 515, 517, 519, 543, 551, 553, 559, 565, 579, 597, 611, 623, 669, 685, 687

Offset: 1

Author

Gus Wiseman, Nov 22 2020

Keywords

• nonn

Examples

			The sequence of terms together with their prime indices begins:
     21: {2,4}     235: {3,15}    393: {2,32}
     39: {2,6}     237: {2,22}    417: {2,34}
     57: {2,8}     247: {6,8}     427: {4,18}
     65: {3,6}     259: {4,12}    445: {3,24}
     87: {2,10}    267: {2,24}    453: {2,36}
     91: {4,6}     299: {6,9}     481: {6,12}
    111: {2,12}    301: {4,14}    489: {2,38}
    115: {3,9}     303: {2,26}    497: {4,20}
    129: {2,14}    305: {3,18}    515: {3,27}
    133: {4,8}     319: {5,10}    517: {5,15}
    159: {2,16}    321: {2,28}    519: {2,40}
    183: {2,18}    339: {2,30}    543: {2,42}
    185: {3,12}    365: {3,21}    551: {8,10}
    203: {4,10}    371: {4,16}    553: {4,22}
    213: {2,20}    377: {6,10}    559: {6,14}
		

Crossrefs

A300912 is the complement in A001358.

A338909 is the not necessarily squarefree version.

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

A005117 lists squarefree numbers.

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

A339005 lists products of pairs of distinct primes of divisible index.

A320656 counts factorizations into squarefree semiprimes.

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.

A338910/A338911 list products of pairs of primes both of odd/even index.

A339003/A339004 list squarefree semiprimes of odd/even index.

Cf. A001221, A001222, A055684, A056239, A112798, A115392, A166237, A167171, A318990, A320892, A320911, A338901.

Programs

Mathematica

Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&&GCD@@PrimePi/@First/@FactorInteger[#]>1&]