login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324855 Lexicographically earliest sequence containing 2 and all squarefree numbers > 2 whose prime indices already belong to the sequence. 2
2, 3, 5, 11, 15, 31, 33, 47, 55, 93, 127, 137, 141, 155, 165, 211, 235, 257, 341, 381, 411, 465, 487, 517, 633, 635, 685, 705, 709, 771, 773, 811, 907, 977, 1023, 1055, 1285, 1297, 1397, 1457, 1461, 1483, 1507, 1551, 1621, 1705, 1905, 2055, 2127, 2293, 2319 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Robert Israel, Table of n, a(n) for n = 1..1567

Gus Wiseman, The rooted identity trees whose Matula-Goebel numbers are the first 64 terms.

EXAMPLE

The sequence of terms together with their prime indices begins:

    2: {1}

    3: {2}

    5: {3}

   11: {5}

   15: {2,3}

   31: {11}

   33: {2,5}

   47: {15}

   55: {3,5}

   93: {2,11}

  127: {31}

  137: {33}

  141: {2,15}

  155: {3,11}

  165: {2,3,5}

  211: {47}

  235: {3,15}

  257: {55}

  341: {5,11}

  381: {2,31}

MAPLE

S:= {2}: count:= 1:

for n from 3 by 2 while count < 100 do

  F:= ifactors(n)[2];

  if max(map(t -> t[2], F))=1 and {seq(numtheory:-pi(t[1]), t=F)} subset S then

     S:= S union {n}; count:= count+1;

  fi

od:

sort(convert(S, list)); # Robert Israel, Mar 22 2019

MATHEMATICA

aQ[n_]:=Switch[n, 1, False, 2, True, _?(!SquareFreeQ[#]&), False, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]]]];

Select[Range[1000], aQ]

CROSSREFS

Cf. A000002, A000720, A001462, A079254, A109298, A112798, A276625, A290822.

Cf. A324697, A324698, A324736, A324748, A324753, A324843, A324850, A324854.

Contains A007097 except for 1.

Sequence in context: A275913 A004680 A230147 * A316467 A282238 A004690

Adjacent sequences:  A324852 A324853 A324854 * A324856 A324857 A324858

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 18 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 08:50 EDT 2019. Contains 328056 sequences. (Running on oeis4.)