The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A331912 Lexicographically earliest sequence of positive integers that have at most one distinct prime index already in the sequence. 13
 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 26, 27, 29, 31, 32, 37, 39, 41, 43, 47, 49, 52, 53, 58, 59, 61, 64, 65, 67, 71, 73, 74, 79, 81, 83, 86, 87, 89, 91, 94, 97, 101, 103, 104, 107, 109, 111, 113, 116, 117, 121, 122, 125, 127, 128, 129, 131, 137 (list; graph; refs; listen; history; text; internal format)
 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. Conjecture: a(n)/A331784(n) -> 1 as n -> infinity. LINKS Gus Wiseman, Plot of A331912(n)/A331784(n) for n = 1..3729. EXAMPLE The sequence of terms together with their prime indices begins:     1: {}              37: {12}              86: {1,14}     2: {1}             39: {2,6}             87: {2,10}     3: {2}             41: {13}              89: {24}     4: {1,1}           43: {14}              91: {4,6}     5: {3}             47: {15}              94: {1,15}     7: {4}             49: {4,4}             97: {25}     8: {1,1,1}         52: {1,1,6}          101: {26}     9: {2,2}           53: {16}             103: {27}    11: {5}             58: {1,10}           104: {1,1,1,6}    13: {6}             59: {17}             107: {28}    16: {1,1,1,1}       61: {18}             109: {29}    17: {7}             64: {1,1,1,1,1,1}    111: {2,12}    19: {8}             65: {3,6}            113: {30}    23: {9}             67: {19}             116: {1,1,10}    25: {3,3}           71: {20}             117: {2,2,6}    26: {1,6}           73: {21}             121: {5,5}    27: {2,2,2}         74: {1,12}           122: {1,18}    29: {10}            79: {22}             125: {3,3,3}    31: {11}            81: {2,2,2,2}        127: {31}    32: {1,1,1,1,1}     83: {23}             128: {1,1,1,1,1,1,1} For example, the prime indices of 117 are {2,2,6}, of which only 2 is already in the sequence, so 117 is in the sequence. MATHEMATICA aQ[n_]:=Length[Select[PrimePi/@First/@If[n==1, {}, FactorInteger[n]], aQ]]<=1; Select[Range[100], aQ] CROSSREFS Contains all prime powers A000961. Numbers S without all prime indices in S are A324694. Numbers S without any prime indices in S are A324695. Numbers S with at most one prime index in S are A331784. Numbers S with exactly one prime index in S are A331785. Numbers S with exactly one distinct prime index in S are A331913. Cf. A000002, A000720, A001222, A001462, A324696, A331683, A331873, A331914. Sequence in context: A322902 A302040 A302036 * A326848 A328957 A030230 Adjacent sequences:  A331909 A331910 A331911 * A331913 A331914 A331915 KEYWORD nonn AUTHOR Gus Wiseman, Feb 01 2020 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.

Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)