A324849 Positive integers divisible by none of their prime indices > 1.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 76, 77, 79, 80, 81, 82, 83, 85, 86, 87

Offset

1,2

Comments

A prime index of n is a number m such that prime(m) divides n.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   3: {2}
   4: {1,1}
   5: {3}
   7: {4}
   8: {1,1,1}
   9: {2,2}
  10: {1,3}
  11: {5}
  13: {6}
  14: {1,4}
  16: {1,1,1,1}
  17: {7}
  19: {8}
  20: {1,1,3}
  21: {2,4}
  22: {1,5}
  23: {9}
  25: {3,3}

Maple

filter:= proc(n) andmap(t -> not ((n/numtheory:-pi(t))::integer), numtheory:-factorset(n) minus {2}) end proc:
select(filter, [$1..200]); # Robert Israel, Mar 20 2019

Mathematica

Select[Range[100], !Or@@Cases[If[#==1, {}, FactorInteger[#]], {p_, _}:>If[p==2, False, Divisible[#, PrimePi[p]]]]&]

Prog

(PARI) is(n) = my(f=factor(n)[, 1]~, idc=[]); for(k=1, #f, idc=concat(idc, [primepi(f[k])])); for(t=1, #idc, if(idc[t]==1, next); if(n%idc[t]==0, return(0))); 1 \\ Felix Fröhlich, Mar 21 2019

Crossrefs

Complement of A324771.

Cf. A003963, A056239, A112798, A120383, A289509, A304360, A306844.

Cf. A324695, A324741, A324743, A324756, A324758, A324765, A324846, A324847, A324848, A324850, A324852, A324853, A324856.

Sequence in context: A307750 A356734 A319630 * A091010 A306528 A116358

Adjacent sequences: A324846 A324847 A324848 * A324850 A324851 A324852

Keyword

nonn

Author

Gus Wiseman, Mar 18 2019

Status

approved