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.
A multiplicative semigroup: if x and y are in the sequence then so is x*y. - Robert Israel, Mar 19 2019
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
4: {1,1}
7: {4}
8: {1,1,1}
14: {1,4}
16: {1,1,1,1}
17: {7}
19: {8}
28: {1,1,4}
32: {1,1,1,1,1}
34: {1,7}
38: {1,8}
43: {14}
49: {4,4}
53: {16}
56: {1,1,1,4}
59: {17}
64: {1,1,1,1,1,1}
67: {19}
68: {1,1,7}
MAPLE
S:= {1}:
for n from 3 to 400 do
if map(numtheory:-pi, numtheory:-factorset(n)) subset S then
S:= S union {n}
fi
od:
sort(convert(S, list)); # Robert Israel, Mar 19 2019
MATHEMATICA
aQ[n_]:=Switch[n, 1, True, 2, False, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]]]];
Select[Range[100], aQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved