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A324846
Positive integers divisible by none of their prime indices.
25
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
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved