A003974 Möbius transform of A003962.

1, 1, 2, 2, 3, 2, 5, 4, 6, 3, 6, 4, 8, 5, 6, 8, 9, 6, 11, 6, 10, 6, 14, 8, 12, 8, 18, 10, 15, 6, 18, 16, 12, 9, 15, 12, 20, 11, 16, 12, 21, 10, 23, 12, 18, 14, 26, 16, 30, 12, 18, 16, 29, 18, 18, 20, 22, 15, 30, 12, 33, 18, 30, 32, 24, 12, 35, 18, 28, 15, 36, 24, 39, 20, 24, 22, 30

Offset

1,3

Links

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

Formula

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

Mathematica

f[p_, e_] := Module[{q = NextPrime[p]}, ((q-1)/2)((q+1)/2)^(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=nextprime(p+1)); ((q-1)/2)*((q+1)/2)^(e-1)); \\ Andrew Howroyd, Nov 16 2025

Crossrefs

Cf. A003962, A003962, A003975, A151800.

Sequence in context: A073311 A347560 A384882 * A065769 A390299 A280264

Adjacent sequences: A003971 A003972 A003973 * A003975 A003976 A003977

Keyword

nonn,easy,mult

Author

Marc LeBrun

Extensions

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

Status

approved