A003960 Fully multiplicative with a(p) = [ (p+1)/2 ] for prime p.

1, 1, 2, 1, 3, 2, 4, 1, 4, 3, 6, 2, 7, 4, 6, 1, 9, 4, 10, 3, 8, 6, 12, 2, 9, 7, 8, 4, 15, 6, 16, 1, 12, 9, 12, 4, 19, 10, 14, 3, 21, 8, 22, 6, 12, 12, 24, 2, 16, 9, 18, 7, 27, 8, 18, 4, 20, 15, 30, 6, 31, 16, 16, 1, 21, 12, 34, 9, 24, 12, 36, 4, 37, 19, 18, 10, 24, 14, 40, 3, 16, 21, 42, 8, 27

Offset

1,3

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Formula

If n = Product p(k)^e(k) then a(n) = Product [ (p(k)+1)/2 ]^e(k).

Multiplicative with a(p^e) = [(p+1)/2]^e. - David W. Wilson, Aug 01 2001

a(n) = 1 iff n is a power of 2 (A000079). - Michel Marcus, Nov 16 2017

Mathematica

f[p_, e_] := Floor[(p+1)/2]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 03 2023 *)

Prog

(PARI) { A003960(n) = my(f); f=factor(n/2^valuation(n, 2)); prod(i=1, matsize(f)[1], ((f[i, 1]+1)/2)^f[i, 2] ); } \\ Max Alekseyev, Jul 27 2017

Crossrefs

Cf. A003970.

Sequence in context: A228731 A163507 A003963 * A243499 A124223 A295908

Adjacent sequences: A003957 A003958 A003959 * A003961 A003962 A003963

Keyword

nonn,easy,mult

Author

Marc LeBrun

Status

approved