A371181 Sorted list of positions of first appearances in the sequence A370820, which counts distinct divisors of prime indices.

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.

Links

Table of n, a(n) for n=1..44.

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.

Cf. A000079, A000720, A000792, A002110, A005179, A007416, A355739, A370348, A370802, A370808, A371165, A371177.

Sequence in context: A033995 A345247 A013917 * A293994 A196419 A056893

Adjacent sequences: A371178 A371179 A371180 * A371182 A371183 A371184

Keyword

nonn

Author

Gus Wiseman, Mar 20 2024

Status

approved