cp's OEIS Frontend

A371131 Least number with exactly n distinct divisors of prime indices. Position of first appearance of n in A370820.

%I A371131 #9 May 02 2024 09:47:10
%S A371131 1,2,3,7,13,53,37,311,89,151,223,2045,281,3241,1163,827,659,9037,1069,
%T A371131 17611,1511,4211,28181,122119,2423,10627,88483,6997,7561,98965,5443,
%U A371131 88099,6473,95603,309073,50543,10271,192709,508051,438979,14323,305107,26203
%N A371131 Least number with exactly n distinct divisors of prime indices. Position of first appearance of n in A370820.
%C A371131 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 A371131 Every nonnegative integer belongs to A370820, so this sequence is infinite.
%C A371131 Are there any terms with more than two prime factors?
%e A371131 The terms together with their prime indices begin:
%e A371131        1: {}
%e A371131        2: {1}
%e A371131        3: {2}
%e A371131        7: {4}
%e A371131       13: {6}
%e A371131       53: {16}
%e A371131       37: {12}
%e A371131      311: {64}
%e A371131       89: {24}
%e A371131      151: {36}
%e A371131      223: {48}
%e A371131     2045: {3,80}
%e A371131      281: {60}
%e A371131     3241: {4,90}
%e A371131     1163: {192}
%e A371131      827: {144}
%e A371131      659: {120}
%e A371131     9037: {4,210}
%e A371131     1069: {180}
%e A371131    17611: {5,252}
%t A371131 rnnm[q_]:=Max@@Select[Range[Min@@q,Max@@q],SubsetQ[q,Range[#]]&];
%t A371131 posfirsts[q_]:=Table[Position[q,n][[1,1]],{n,Min@@q,rnnm[q]}];
%t A371131 posfirsts[Table[Length[Union @@ Divisors/@PrimePi/@First/@If[n==1, {},FactorInteger[n]]],{n,1000}]]
%o A371131 (PARI) f(n) = my(list=List(), f=factor(n)); for (i=1, #f~, fordiv(primepi(f[i,1]), d, listput(list, d))); #Set(list); \\ A370820
%o A371131 a(n) = my(k=1); while (f(k) != n, k++); k; \\ _Michel Marcus_, May 02 2024
%Y A371131 Counting prime factors instead of divisors (see A303975) gives A062447(>0).
%Y A371131 The sorted version is A371181.
%Y A371131 A000005 counts divisors.
%Y A371131 A001221 counts distinct prime factors.
%Y A371131 A003963 gives product of prime indices.
%Y A371131 A027746 lists prime factors, A112798 indices, length A001222.
%Y A371131 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A371131 A355741 counts choices of a prime factor of each prime index.
%Y A371131 Cf. A000720, A000792, A005179, A007416, A355739, A370348, A370802, A370808, A371130, A371165, A371177.
%K A371131 nonn
%O A371131 0,2
%A A371131 _Gus Wiseman_, Mar 20 2024