cp's OEIS Frontend

A371288 Numbers whose distinct prime indices form the set of divisors of some positive integer.

%I A371288 #12 Aug 26 2024 09:55:39
%S A371288 2,4,6,8,10,12,16,18,20,22,24,32,34,36,40,42,44,48,50,54,62,64,68,72,
%T A371288 80,82,84,88,96,100,108,118,124,126,128,134,136,144,160,162,164,166,
%U A371288 168,176,192,200,216,218,230,236,242,248,250,252,254,256,268,272,288
%N A371288 Numbers whose distinct prime indices form the set of divisors of some positive integer.
%C A371288 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.
%H A371288 Joseph Likar, <a href="/A371288/b371288.txt">Table of n, a(n) for n = 1..10000</a>
%e A371288 The prime indices of 694782 are {1,2,2,5,5,5,10} with distinct elements {1,2,5,10}, which form the set of divisors of 10, so 694782 is in the sequence.
%e A371288 The terms together with their prime indices begin:
%e A371288     2: {1}
%e A371288     4: {1,1}
%e A371288     6: {1,2}
%e A371288     8: {1,1,1}
%e A371288    10: {1,3}
%e A371288    12: {1,1,2}
%e A371288    16: {1,1,1,1}
%e A371288    18: {1,2,2}
%e A371288    20: {1,1,3}
%e A371288    22: {1,5}
%e A371288    24: {1,1,1,2}
%e A371288    32: {1,1,1,1,1}
%e A371288    34: {1,7}
%e A371288    36: {1,1,2,2}
%e A371288    40: {1,1,1,3}
%e A371288    42: {1,2,4}
%e A371288    44: {1,1,5}
%e A371288    48: {1,1,1,1,2}
%t A371288 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A371288 Select[Range[100],Union[prix[#]]==Divisors[Max@@prix[#]]&]
%Y A371288 The squarefree case is A371283, unsorted version A275700.
%Y A371288 Partitions of this type are counted by A371284, strict A054973.
%Y A371288 Products of squarefree terms are A371286, unsorted version A371285.
%Y A371288 A000005 counts divisors.
%Y A371288 A001221 counts distinct prime factors.
%Y A371288 A027746 lists prime factors, indices A112798, length A001222.
%Y A371288 Cf. A000720, A003963, A005179, A007416, A034729, A370820, A371131, A371177.
%K A371288 nonn
%O A371288 1,1
%A A371288 _Gus Wiseman_, Mar 22 2024