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%I #7 Mar 21 2024 17:46:32
%S 1,2,3,7,13,37,53,89,151,223,281,311,659,827,1069,1163,1511,2045,2423,
%T 3241,4211,5443,6473,6997,7561,9037,10271,10627,14323,17611,26203,
%U 28181,33613,50543,88099,88483,95603,98965,122119,168281,192709,305107,309073,420167
%N Sorted list of positions of first appearances in the sequence A370820, which counts distinct divisors of prime indices.
%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.
%e The terms together with their prime indices begin:
%e 1: {}
%e 2: {1}
%e 3: {2}
%e 7: {4}
%e 13: {6}
%e 37: {12}
%e 53: {16}
%e 89: {24}
%e 151: {36}
%e 223: {48}
%e 281: {60}
%e 311: {64}
%e 659: {120}
%e 827: {144}
%e 1069: {180}
%e 1163: {192}
%e 1511: {240}
%e 2045: {3,80}
%e 2423: {360}
%e 3241: {4,90}
%e 4211: {576}
%e 5443: {720}
%e 6473: {840}
%e 6997: {900}
%e 7561: {960}
%e 9037: {4,210}
%t rnnm[q_]:=Max@@Select[Range[Min@@q,Max@@q],SubsetQ[q,Range[#]]&];
%t posfirsts[q_]:=Table[Position[q,n][[1,1]],{n,Min@@q,rnnm[q]}];
%t posfirsts[Table[Length[Union @@ Divisors/@PrimePi/@First/@If[n==1,{},FactorInteger[n]]],{n,1000}]]//Sort
%Y Counting prime factors instead of divisors (see A303975) gives A062447(>0).
%Y The unsorted version is A371131.
%Y A000005 counts divisors.
%Y A001221 counts distinct prime factors.
%Y A003963 gives product of prime indices.
%Y A027746 lists prime factors, A112798 indices, length A001222.
%Y A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A355741 counts choices of a prime factor of each prime index.
%Y Cf. A000079, A000720, A000792, A002110, A005179, A007416, A355739, A370348, A370802, A370808, A371165, A371177.
%K nonn
%O 1,2
%A _Gus Wiseman_, Mar 20 2024
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