OFFSET
1,5
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..10000 (a(3..10^4) from Michel Marcus), Apr 13 2022
FORMULA
From Bernard Schott, Mar 23 2022: (Start)
a(n) = 1 iff n is in A146566.
a(n) = n - 2 iff n is an odd prime (A065091). (End)
From M. F. Hasler, Apr 06 2022: (Start)
More generally, explaining the "rays" visible in the graph:
a(n) = n - d with d = 2^w if n is the product of w distinct odd primes, and with d = e+1 if n = p^e, prime p not dividing e+1.
a(n) = n/2 - d with d = 3 if n = 4*p, prime p > 3, and with d = 2^w if n = 2*k where k is the product of w distinct odd primes.
a(n) = n/3 - 2^w if n = 3*p^2 with prime p > 3, w = 1, or if n = 9*k where k is the product of w distinct primes > 3.
a(n) = n/5 - d with d = 2 if n = 5^4*p, odd prime p <> 5, or with d = 4 if n = 3^4*5*p, prime p > 5, not p == 4 (mod 5).
a(n) = n/6 - d with d = 2 if n = 18*p, or with d = 4 if n = 18*p^3 or 18*p*q, primes q > p > 3.
a(n) = (p - 1)/2^m if n = 8*p, where m = max { m <= 3 : 2^m divides p-1 } = min {valuation(p-1, 2), 3}.
a(n) = (n - 12)/9 if n = 3*p^2*q, p and q distinct primes > 3 and q == 1 (mod 3). (End)
MATHEMATICA
a[n_] := Numerator[1/DivisorSigma[0, n] - 1/n]; Array[a, 100] (* Amiram Eldar, Apr 13 2022 *)
PROG
(PARI) a(n) = my(d=numdiv(n)); denominator(n*d/(n-d));
(PARI) apply( {A352483(n)=numerator(1/numdiv(n)-1/n)}, [3..99]) \\ M. F. Hasler, Apr 07 2022
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Michel Marcus, Mar 18 2022
EXTENSIONS
Definition changed to include indices 1 and 2 by M. F. Hasler, Apr 07 2022
STATUS
approved