OFFSET
1,60
COMMENTS
The indices of terms greater than 1 are {60, 84, 90, 120, 126, 132, 140, 150, ...}.
First term greater than 2 is a(1801800) = 3. In general, the first appearance of k is a(A182856(k)) = k.
The prime signature of n (row n of A118914) is the multiset of prime multiplicities in n.
We define the k-th omega of n to be Omega(red^{k-1}(n)) where Omega = A001222 and red^{k} is the k-th functional iteration of A181819. The first three omegas are A001222, A001221, A071625, and this sequence is the fourth. The zeroth omega is not uniquely determined from prime signature, but one possible choice is A056239 (sum of prime indices).
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
FORMULA
EXAMPLE
The prime signature of 1286485200 is {1, 1, 1, 2, 2, 3, 4}, in which 1 appears three times, two appears twice, and 3 and 4 both appear once, so there are 3 distinct multiplicities {1, 2, 3} and hence a(1286485200) = 3.
MATHEMATICA
red[n_]:=Times@@Prime/@Last/@If[n==1, {}, FactorInteger[n]];
Table[PrimeNu[red[red[n]]], {n, 200}]
PROG
(PARI) a(n) = my(e=factor(n)[, 2], s = Set(e), m=Map(), v=vector(#s)); for(i=1, #s, mapput(m, s[i], i)); for(i=1, #e, v[mapget(m, e[i])]++); #Set(v) \\ David A. Corneth, Jan 02 2019
(PARI)
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 02 2019
EXTENSIONS
More terms from Antti Karttunen, Jan 03 2019
STATUS
approved