cp's OEIS Frontend

A338468 Odd squarefree numbers whose prime indices have no common divisor > 1.

%I A338468 #10 Nov 05 2020 22:56:31
%S A338468 15,33,35,51,55,69,77,85,93,95,105,119,123,141,143,145,155,161,165,
%T A338468 177,187,195,201,205,209,215,217,219,221,231,249,253,255,265,285,287,
%U A338468 291,295,309,323,327,329,335,341,345,355,357,381,385,391,395,403,407,411
%N A338468 Odd squarefree numbers whose prime indices have no common divisor > 1.
%C A338468 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 A338468 Also Heinz numbers of relatively prime strict integer partitions with no 1's (A337452). 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 A338468 The sequence of terms together with their prime indices begins:
%e A338468      15: {2,3}      145: {3,10}     249: {2,23}     355: {3,20}
%e A338468      33: {2,5}      155: {3,11}     253: {5,9}      357: {2,4,7}
%e A338468      35: {3,4}      161: {4,9}      255: {2,3,7}    381: {2,31}
%e A338468      51: {2,7}      165: {2,3,5}    265: {3,16}     385: {3,4,5}
%e A338468      55: {3,5}      177: {2,17}     285: {2,3,8}    391: {7,9}
%e A338468      69: {2,9}      187: {5,7}      287: {4,13}     395: {3,22}
%e A338468      77: {4,5}      195: {2,3,6}    291: {2,25}     403: {6,11}
%e A338468      85: {3,7}      201: {2,19}     295: {3,17}     407: {5,12}
%e A338468      93: {2,11}     205: {3,13}     309: {2,27}     411: {2,33}
%e A338468      95: {3,8}      209: {5,8}      323: {7,8}      413: {4,17}
%e A338468     105: {2,3,4}    215: {3,14}     327: {2,29}     415: {3,23}
%e A338468     119: {4,7}      217: {4,11}     329: {4,15}     429: {2,5,6}
%e A338468     123: {2,13}     219: {2,21}     335: {3,19}     435: {2,3,10}
%e A338468     141: {2,15}     221: {6,7}      341: {5,11}     437: {8,9}
%e A338468     143: {5,6}      231: {2,4,5}    345: {2,3,9}    447: {2,35}
%t A338468 Select[Range[1,100,2],SquareFreeQ[#]&&GCD@@PrimePi/@First/@FactorInteger[#]==1&]
%Y A338468 A302568 is the prime or pairwise coprime version, counted by A007359.
%Y A338468 A302697 is not required to be squarefree, counted by A302698 (ordered version: A337450).
%Y A338468 A302796 allows evens, counted by A078374 (ordered version: A332004).
%Y A338468 A337452 counts partitions with these Heinz numbers (ordered version: A337451).
%Y A338468 A337984 is the pairwise coprime version, counted by A337485 (ordered version: A337697).
%Y A338468 A005117 lists squarefree numbers.
%Y A338468 A005408 lists odd numbers.
%Y A338468 A056911 lists odd squarefree numbers.
%Y A338468 A289509 lists Heinz numbers of relatively prime partitions, counted by A000837 (ordered version: A000740).
%Y A338468 Cf. A000010, A007359, A051424, A055684, A056239, A101268, A289508, A302505, A302569, A302696, A302798, A337694.
%K A338468 nonn
%O A338468 1,1
%A A338468 _Gus Wiseman_, Oct 29 2020