

A370810


Numbers n such that only one set can be obtained by choosing a different divisor of each prime index of n.


13



1, 2, 6, 9, 10, 22, 25, 30, 34, 42, 45, 62, 63, 66, 75, 82, 98, 99, 102, 110, 118, 121, 134, 147, 153, 166, 170, 186, 210, 218, 230, 246, 254, 275, 279, 289, 310, 314, 315, 330, 343, 354, 358, 363, 369, 374, 382, 390, 402, 410, 422, 425, 462, 482, 490, 495
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OFFSET

1,2


COMMENTS

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.


LINKS



EXAMPLE

The prime indices of 6591 are {2,6,6,6}, for which the only choice is {1,2,3,6}, so 6591 is in the sequence.
The terms together with their prime indices begin:
1: {}
2: {1}
6: {1,2}
9: {2,2}
10: {1,3}
22: {1,5}
25: {3,3}
30: {1,2,3}
34: {1,7}
42: {1,2,4}
45: {2,2,3}
62: {1,11}
63: {2,2,4}
66: {1,2,5}
75: {2,3,3}
82: {1,13}
98: {1,4,4}
99: {2,2,5}
102: {1,2,7}
110: {1,3,5}


MATHEMATICA

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Length[Union[Sort /@ Select[Tuples[Divisors/@prix[#]], UnsameQ@@#&]]]==1&]


CROSSREFS

A355731 counts choices of a divisor of each prime index, firsts A355732.
A370814 counts factorizations with choosable divisors, complement A370813.


KEYWORD

nonn,changed


AUTHOR



STATUS

approved



