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

Author

Marc LeBrun

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A003970.

Programs

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 *)

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

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