A338468 - OEIS

%I #10 Nov 05 2020 22:56:31

%S 15,33,35,51,55,69,77,85,93,95,105,119,123,141,143,145,155,161,165,

%T 177,187,195,201,205,209,215,217,219,221,231,249,253,255,265,285,287,

%U 291,295,309,323,327,329,335,341,345,355,357,381,385,391,395,403,407,411

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

%C 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 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 The sequence of terms together with their prime indices begins:

%e      15: {2,3}      145: {3,10}     249: {2,23}     355: {3,20}

%e      33: {2,5}      155: {3,11}     253: {5,9}      357: {2,4,7}

%e      35: {3,4}      161: {4,9}      255: {2,3,7}    381: {2,31}

%e      51: {2,7}      165: {2,3,5}    265: {3,16}     385: {3,4,5}

%e      55: {3,5}      177: {2,17}     285: {2,3,8}    391: {7,9}

%e      69: {2,9}      187: {5,7}      287: {4,13}     395: {3,22}

%e      77: {4,5}      195: {2,3,6}    291: {2,25}     403: {6,11}

%e      85: {3,7}      201: {2,19}     295: {3,17}     407: {5,12}

%e      93: {2,11}     205: {3,13}     309: {2,27}     411: {2,33}

%e      95: {3,8}      209: {5,8}      323: {7,8}      413: {4,17}

%e     105: {2,3,4}    215: {3,14}     327: {2,29}     415: {3,23}

%e     119: {4,7}      217: {4,11}     329: {4,15}     429: {2,5,6}

%e     123: {2,13}     219: {2,21}     335: {3,19}     435: {2,3,10}

%e     141: {2,15}     221: {6,7}      341: {5,11}     437: {8,9}

%e     143: {5,6}      231: {2,4,5}    345: {2,3,9}    447: {2,35}

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

%Y A302568 is the prime or pairwise coprime version, counted by A007359.

%Y A302697 is not required to be squarefree, counted by A302698 (ordered version: A337450).

%Y A302796 allows evens, counted by A078374 (ordered version: A332004).

%Y A337452 counts partitions with these Heinz numbers (ordered version: A337451).

%Y A337984 is the pairwise coprime version, counted by A337485 (ordered version: A337697).

%Y A005117 lists squarefree numbers.

%Y A005408 lists odd numbers.

%Y A056911 lists odd squarefree numbers.

%Y A289509 lists Heinz numbers of relatively prime partitions, counted by A000837 (ordered version: A000740).

%Y Cf. A000010, A007359, A051424, A055684, A056239, A101268, A289508, A302505, A302569, A302696, A302798, A337694.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 29 2020