A003977 Inverse Möbius transform of A003963.

1, 2, 3, 3, 4, 6, 5, 4, 7, 8, 6, 9, 7, 10, 12, 5, 8, 14, 9, 12, 15, 12, 10, 12, 13, 14, 15, 15, 11, 24, 12, 6, 18, 16, 20, 21, 13, 18, 21, 16, 14, 30, 15, 18, 28, 20, 16, 15, 21, 26, 24, 21, 17, 30, 24, 20, 27, 22, 18, 36, 19, 24, 35, 7, 28, 36, 20, 24, 30, 40, 21, 28, 22, 26

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = e+1 if p = 2; (q^(e+1)-1)/(q-1) if p > 2; where q = pi(p) = A000720(p). - David W. Wilson, Sep 01 2001

Mathematica

f[p_, e_] := Module[{q = PrimePi[p]}, (q^(e+1)-1)/(q-1)]; f[2, e_] := e+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)); prod(i=1, #f~, my([p, e]=f[i, ], q=primepi(p)); if(q==1, 1 + e, (q^(e+1)-1)/(q-1))); \\ Andrew Howroyd, Nov 18 2025

Crossrefs

Cf. A000720, A003963.

Sequence in context: A358298 A347712 A159999 * A003971 A349371 A282442

Adjacent sequences: A003974 A003975 A003976 * A003978 A003979 A003980

Keyword

nonn,easy,mult

Author

Marc LeBrun

Extensions

More terms from David W. Wilson, Aug 29 2001

Status

approved