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

Author

Gus Wiseman, Mar 18 2019

Keywords

• nonn

Comments

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

Examples

			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}
		

Links

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

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.

Programs

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]]]]&]

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