OFFSET
1,4
COMMENTS
This sequence can be used as a filter. It matches at least to the following sequences related to the counting of various non-unitary prime divisors:
For all i, j:
An encoding of the prime signature of A057521(n), the powerful part of n. - Peter Munn, Apr 06 2024
LINKS
FORMULA
a(1) = 1; for n>1, if n = Product prime(i)^e(i), then a(n) = Product A008578(e(i)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + 1/p^2 + Sum_{k>=1} (prime(k+1)-prime(k))/p^(k+2)) = 2.208... . - Amiram Eldar, Nov 18 2022
MATHEMATICA
Array[Apply[Times, FactorInteger[#] /. {p_, e_} /; p > 0 :> Which[p == 1, 1, e == 1, 1, True, Prime[e - 1]]] &, 128] (* Michael De Vlieger, Nov 29 2017 *)
PROG
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
Antti Karttunen, Nov 29 2017
STATUS
approved