cp's OEIS Frontend

A337987 Odd numbers whose distinct prime indices are pairwise coprime, where a singleton is not considered coprime unless it is (1).

%I A337987 #6 Nov 01 2020 01:47:04
%S A337987 15,33,35,45,51,55,69,75,77,85,93,95,99,119,123,135,141,143,145,153,
%T A337987 155,161,165,175,177,187,201,205,207,209,215,217,219,221,225,245,249,
%U A337987 253,255,265,275,279,287,291,295,297,309,323,327,329,335,341,355,363,369
%N A337987 Odd numbers whose distinct prime indices are pairwise coprime, where a singleton is not considered coprime unless it is (1).
%C A337987 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A337987 Also Heinz numbers of integer partitions with no 1's whose distinct parts are pairwise coprime (A338315). The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
%e A337987 The sequence of terms together with their prime indices begins:
%e A337987      15: {2,3}      135: {2,2,2,3}    215: {3,14}
%e A337987      33: {2,5}      141: {2,15}       217: {4,11}
%e A337987      35: {3,4}      143: {5,6}        219: {2,21}
%e A337987      45: {2,2,3}    145: {3,10}       221: {6,7}
%e A337987      51: {2,7}      153: {2,2,7}      225: {2,2,3,3}
%e A337987      55: {3,5}      155: {3,11}       245: {3,4,4}
%e A337987      69: {2,9}      161: {4,9}        249: {2,23}
%e A337987      75: {2,3,3}    165: {2,3,5}      253: {5,9}
%e A337987      77: {4,5}      175: {3,3,4}      255: {2,3,7}
%e A337987      85: {3,7}      177: {2,17}       265: {3,16}
%e A337987      93: {2,11}     187: {5,7}        275: {3,3,5}
%e A337987      95: {3,8}      201: {2,19}       279: {2,2,11}
%e A337987      99: {2,2,5}    205: {3,13}       287: {4,13}
%e A337987     119: {4,7}      207: {2,2,9}      291: {2,25}
%e A337987     123: {2,13}     209: {5,8}        295: {3,17}
%t A337987 Select[Range[1,100,2],CoprimeQ@@Union[PrimePi/@First/@FactorInteger[#]]&]
%Y A337987 A304711 is the not necessarily odd version, with squarefree case A302797.
%Y A337987 A337694 is a pairwise non-coprime instead of pairwise coprime version.
%Y A337987 A337984 is the squarefree case.
%Y A337987 A338315 counts the partitions with these Heinz numbers.
%Y A337987 A338316 considers singletons coprime.
%Y A337987 A007359 counts partitions into singleton or pairwise coprime parts with no 1's, with Heinz numbers A302568.
%Y A337987 A304709 counts partitions whose distinct parts are pairwise coprime.
%Y A337987 A327516 counts pairwise coprime partitions, with Heinz numbers A302696.
%Y A337987 A337462 counts pairwise coprime compositions, ranked by A333227.
%Y A337987 A337561 counts pairwise coprime strict compositions.
%Y A337987 A337665 counts compositions whose distinct parts are pairwise coprime, ranked by A333228.
%Y A337987 A337667 counts pairwise non-coprime compositions, ranked by A337666.
%Y A337987 A337697 counts pairwise coprime compositions with no 1's.
%Y A337987 A318717 counts pairwise non-coprime strict partitions, with Heinz numbers A318719.
%Y A337987 Cf. A005408, A051424, A056239, A087087, A112798, A200976, A289508, A289509, A302569, A303282, A328867, A337485.
%K A337987 nonn
%O A337987 1,1
%A A337987 _Gus Wiseman_, Oct 23 2020