A339003 Numbers of the form prime(x) * prime(y) where x and y are distinct and both odd.

10, 22, 34, 46, 55, 62, 82, 85, 94, 115, 118, 134, 146, 155, 166, 187, 194, 205, 206, 218, 235, 253, 254, 274, 295, 298, 314, 334, 335, 341, 358, 365, 382, 391, 394, 415, 422, 451, 454, 466, 482, 485, 514, 515, 517, 527, 538, 545, 554, 566, 614, 626, 635, 649

Offset

1,1

Comments

The squarefree semiprimes in A332822. - Peter Munn, Dec 25 2020

Links

Table of n, a(n) for n=1..54.

Formula

Numbers m such that A001221(m) = A001222(m) = A195017(m) = 2. - Peter Munn, Dec 31 2020

Example

The sequence of terms together with their prime indices begins:
     10: {1,3}     187: {5,7}     358: {1,41}    527: {7,11}
     22: {1,5}     194: {1,25}    365: {3,21}    538: {1,57}
     34: {1,7}     205: {3,13}    382: {1,43}    545: {3,29}
     46: {1,9}     206: {1,27}    391: {7,9}     554: {1,59}
     55: {3,5}     218: {1,29}    394: {1,45}    566: {1,61}
     62: {1,11}    235: {3,15}    415: {3,23}    614: {1,63}
     82: {1,13}    253: {5,9}     422: {1,47}    626: {1,65}
     85: {3,7}     254: {1,31}    451: {5,13}    635: {3,31}
     94: {1,15}    274: {1,33}    454: {1,49}    649: {5,17}
    115: {3,9}     295: {3,17}    466: {1,51}    662: {1,67}
    118: {1,17}    298: {1,35}    482: {1,53}    685: {3,33}
    134: {1,19}    314: {1,37}    485: {3,25}    694: {1,69}
    146: {1,21}    334: {1,39}    514: {1,55}    697: {7,13}
    155: {3,11}    335: {3,19}    515: {3,27}    706: {1,71}
    166: {1,23}    341: {5,11}    517: {5,15}    713: {9,11}

Mathematica

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

Crossrefs

A338910 is the not necessarily squarefree version.

A339004 is the even instead of odd version.

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

A005117 lists squarefree numbers.

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

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

A300912 lists products of two primes of relatively prime 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.

A338904 groups semiprimes by weight.

A338906/A338907 list semiprimes of even/odd weight.

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

A339005 lists products of two distinct primes of divisible index.

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

Subsequence of A332822.

Sequence in context: A053361 A214153 A179887 * A017641 A232540 A217573

Adjacent sequences: A339000 A339001 A339002 * A339004 A339005 A339006

Keyword

nonn

Author

Gus Wiseman, Nov 21 2020

Status

approved