cp's OEIS Frontend

A339005 Numbers of the form prime(x) * prime(y) where x properly divides y. Squarefree semiprimes with divisible prime indices.

%I A339005 #4 Dec 07 2020 01:48:53
%S A339005 6,10,14,21,22,26,34,38,39,46,57,58,62,65,74,82,86,87,94,106,111,115,
%T A339005 118,122,129,133,134,142,146,158,159,166,178,183,185,194,202,206,213,
%U A339005 214,218,226,235,237,254,259,262,267,274,278,298,302,303,305,314,319
%N A339005 Numbers of the form prime(x) * prime(y) where x properly divides y. Squarefree semiprimes with divisible prime indices.
%C A339005 A squarefree semiprime (A006881) 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.
%F A339005 Equals A318990 \ A000290.
%e A339005 The sequence of terms together with their prime indices begins:
%e A339005     6: {1,2}    82: {1,13}  159: {2,16}  259: {4,12}
%e A339005    10: {1,3}    86: {1,14}  166: {1,23}  262: {1,32}
%e A339005    14: {1,4}    87: {2,10}  178: {1,24}  267: {2,24}
%e A339005    21: {2,4}    94: {1,15}  183: {2,18}  274: {1,33}
%e A339005    22: {1,5}   106: {1,16}  185: {3,12}  278: {1,34}
%e A339005    26: {1,6}   111: {2,12}  194: {1,25}  298: {1,35}
%e A339005    34: {1,7}   115: {3,9}   202: {1,26}  302: {1,36}
%e A339005    38: {1,8}   118: {1,17}  206: {1,27}  303: {2,26}
%e A339005    39: {2,6}   122: {1,18}  213: {2,20}  305: {3,18}
%e A339005    46: {1,9}   129: {2,14}  214: {1,28}  314: {1,37}
%e A339005    57: {2,8}   133: {4,8}   218: {1,29}  319: {5,10}
%e A339005    58: {1,10}  134: {1,19}  226: {1,30}  321: {2,28}
%e A339005    62: {1,11}  142: {1,20}  235: {3,15}  326: {1,38}
%e A339005    65: {3,6}   146: {1,21}  237: {2,22}  334: {1,39}
%e A339005    74: {1,12}  158: {1,22}  254: {1,31}  339: {2,30}
%t A339005 Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&& Divisible@@Reverse[PrimePi/@First/@FactorInteger[#]]&]
%Y A339005 A300912 is the version for relative primality.
%Y A339005 A318990 is the not necessarily squarefree version.
%Y A339005 A339002 is the version for non-relative primality.
%Y A339005 A339003 is the version for odd indices.
%Y A339005 A339004 is the version for even indices
%Y A339005 A001358 lists semiprimes.
%Y A339005 A005117 lists squarefree numbers.
%Y A339005 A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A339005 A320655 counts factorizations into semiprimes.
%Y A339005 A320656 counts factorizations into squarefree semiprimes.
%Y A339005 A338898/A338912/A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A339005 A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A339005 Cf. A001221, A112798, A166237, A320911, A338901, A338904, A338909.
%K A339005 nonn
%O A339005 1,1
%A A339005 _Gus Wiseman_, Dec 05 2020