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A371181
Sorted list of positions of first appearances in the sequence A370820, which counts distinct divisors of prime indices.
3
1, 2, 3, 7, 13, 37, 53, 89, 151, 223, 281, 311, 659, 827, 1069, 1163, 1511, 2045, 2423, 3241, 4211, 5443, 6473, 6997, 7561, 9037, 10271, 10627, 14323, 17611, 26203, 28181, 33613, 50543, 88099, 88483, 95603, 98965, 122119, 168281, 192709, 305107, 309073, 420167
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.
EXAMPLE
The terms together with their prime indices begin:
1: {}
2: {1}
3: {2}
7: {4}
13: {6}
37: {12}
53: {16}
89: {24}
151: {36}
223: {48}
281: {60}
311: {64}
659: {120}
827: {144}
1069: {180}
1163: {192}
1511: {240}
2045: {3,80}
2423: {360}
3241: {4,90}
4211: {576}
5443: {720}
6473: {840}
6997: {900}
7561: {960}
9037: {4,210}
MATHEMATICA
rnnm[q_]:=Max@@Select[Range[Min@@q, Max@@q], SubsetQ[q, Range[#]]&];
posfirsts[q_]:=Table[Position[q, n][[1, 1]], {n, Min@@q, rnnm[q]}];
posfirsts[Table[Length[Union @@ Divisors/@PrimePi/@First/@If[n==1, {}, FactorInteger[n]]], {n, 1000}]]//Sort
CROSSREFS
Counting prime factors instead of divisors (see A303975) gives A062447(>0).
The unsorted version is A371131.
A000005 counts divisors.
A001221 counts distinct prime factors.
A003963 gives product of prime indices.
A027746 lists prime factors, A112798 indices, length A001222.
A355731 counts choices of a divisor of each prime index, firsts A355732.
A355741 counts choices of a prime factor of each prime index.
Sequence in context: A345247 A373894 A013917 * A293994 A196419 A056893
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 20 2024
STATUS
approved