A003975 Inverse Möbius transform of A003962.

1, 3, 4, 7, 5, 12, 7, 15, 13, 15, 8, 28, 10, 21, 20, 31, 11, 39, 13, 35, 28, 24, 16, 60, 21, 30, 40, 49, 17, 60, 20, 63, 32, 33, 35, 91, 22, 39, 40, 75, 23, 84, 25, 56, 65, 48, 28, 124, 43, 63, 44, 70, 31, 120, 40, 105, 52, 51, 32, 140, 35, 60, 91, 127, 50, 96, 37, 77, 64

Offset

1,2

Links

Table of n, a(n) for n=1..69.

Formula

Multiplicative with a(p^e) = (q^(e+1)-1)/(q-1) where q = (nextPrime(p)+1)/2. - David W. Wilson, Sep 01 2001; corrected by Michel Marcus, Feb 26 2015

Maple

f:= proc(n) local q, r, t;
  r:= 1;
  for t in ifactors(n)[2] do
    q:= (nextprime(t[1])+1)/2;
    r:= r*(q^(t[2]+1)-1)/(q-1);
  od:
  r
end proc:
seq(f(n), n=1..100); # Robert Israel, Feb 26 2015

Mathematica

f[p_, e_] := Module[{q = (NextPrime[p] + 1)/2}, (q^(e+1)-1)/(q-1)]; a[n_] := Times @@ f @@@ FactorInteger[n]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Sep 04 2023 *)

Prog

(PARI) a(n) = {my(f=factor(n)); for (i=1, #f~, q = (nextprime(f[i, 1] + 1)+1)/2; f[i, 1] = (q^(f[i, 2]+1) - 1)/(q-1); f[i, 2] = 1); factorback(f); } \\ Michel Marcus, Feb 26 2015

Crossrefs

Cf. A003962, A151800.

Sequence in context: A254931 A338285 A050197 * A285896 A082226 A010613

Adjacent sequences: A003972 A003973 A003974 * A003976 A003977 A003978

Keyword

nonn,easy,mult

Author

Marc LeBrun

Extensions

Corrected and extended by David W. Wilson, Aug 29 2001

Status

approved