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A324846 Positive integers divisible by none of their prime indices. 24
1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 117, 121, 123, 125, 127, 129, 131, 133, 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. For example, the prime indices of 5673 are {2,11,18}, none of which divides 5673, so 5673 belongs to the sequence.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

EXAMPLE

The sequence of terms together with their prime indices begins:

   1: {}

   3: {2}

   5: {3}

   7: {4}

   9: {2,2}

  11: {5}

  13: {6}

  17: {7}

  19: {8}

  21: {2,4}

  23: {9}

  25: {3,3}

  27: {2,2,2}

  29: {10}

  31: {11}

  33: {2,5}

  35: {3,4}

  37: {12}

  39: {2,6}

MAPLE

q:= n-> ormap(i-> irem(n, numtheory[pi](i[1]))=0, ifactors(n)[2]):

remove(q, [$1..200])[];  # Alois P. Heinz, Mar 19 2019

MATHEMATICA

Select[Range[100], !Or@@Cases[If[#==1, {}, FactorInteger[#]], {p_, _}:>Divisible[#, PrimePi[p]]]&]

PROG

(PARI) isok(n) = {my(f = factor(n)[, 1]); for (k=1, #f, if (!(n % primepi(f[k])), return (0)); ); return (1); } \\ Michel Marcus, Mar 19 2019

CROSSREFS

Complement of A324847.

Cf. A000720, A001222, A003963, A056239, A112798, A120383, A289509, A290822, A304360, A306844.

Cf. A324695, A324741, A324743, A324756, A324758, A324765, A324848, A324849, A324850, A324852, A324853.

Sequence in context: A033040 A200982 A084820 * A324760 A324761 A244579

Adjacent sequences:  A324843 A324844 A324845 * A324847 A324848 A324849

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 18 2019

STATUS

approved

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Last modified April 1 02:10 EDT 2020. Contains 333153 sequences. (Running on oeis4.)