OFFSET
1,21
COMMENTS
a(n) = m first occurs at n = A098918(m). - Robert Israel, Feb 03 2020
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..131072 (terms 1..10000 from Robert Israel)
FORMULA
From Antti Karttunen, May 12 2022: (Start)
a(n) = a(2*n) = a(A000265(n)).
a(n) <= A331410(n). (End)
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A173898 = 0.516454... . - Amiram Eldar, Dec 31 2023
EXAMPLE
a(21)=2 because 1, 3, 7 and 21 are divisors of 21. Then 21 has two divisors that are Mersenne primes (A000668): 3 and 7.
MAPLE
N:= 100: # for a(1)..a(N)
V:= Vector(N):
for i from 1 do
m:= numtheory:-mersenne([i]);
if m > N then break fi;
for j from m by m to N do
V[j]:= V[j]+1
od od:
convert(V, list); # Robert Israel, Feb 03 2020
PROG
(PARI) A147645(n) = { my(m=3, s=0); while(m<=n, s += (isprime(m)*!(n%m)); m += (m+1)); (s); }; \\ Antti Karttunen, May 12 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Nov 09 2008
STATUS
approved