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 A352483 Numerator of 1/d - 1/n = (n-d)/(n*d) where d is the number of divisors of n (A000005). 6
 0, 0, 1, 1, 3, 1, 5, 1, 2, 3, 9, 1, 11, 5, 11, 11, 15, 1, 17, 7, 17, 9, 21, 1, 22, 11, 23, 11, 27, 11, 29, 13, 29, 15, 31, 1, 35, 17, 35, 1, 39, 17, 41, 19, 13, 21, 45, 19, 46, 11, 47, 23, 51, 23, 51, 3, 53, 27, 57, 1, 59, 29, 19, 57, 61, 29, 65, 31, 65, 31, 69, 5, 71, 35, 23, 35, 73 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000005, A049820, A065091, A146566, A352482 (denominator). Sequence in context: A134700 A085407 A325523 * A016475 A037227 A056753 Adjacent sequences: A352480 A352481 A352482 * A352484 A352485 A352486 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

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Last modified August 9 21:53 EDT 2024. Contains 375044 sequences. (Running on oeis4.)