A147645 Number of distinct Mersenne primes dividing n.
0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 1, 1, 0
Offset: 1
Examples
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.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..131072 (terms 1..10000 from Robert Israel)
Crossrefs
Programs
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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 -
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
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
Comments