A371181 - OEIS

%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