A066504 Sum of n/p^k over all maximal prime-power divisors of n.

0, 1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 7, 1, 9, 8, 1, 1, 11, 1, 9, 10, 13, 1, 11, 1, 15, 1, 11, 1, 31, 1, 1, 14, 19, 12, 13, 1, 21, 16, 13, 1, 41, 1, 15, 14, 25, 1, 19, 1, 27, 20, 17, 1, 29, 16, 15, 22, 31, 1, 47, 1, 33, 16, 1, 18, 61, 1, 21, 26, 59, 1, 17, 1, 39, 28, 23, 18, 71, 1, 21, 1, 43, 1

Offset: 1

Author

Reinhard Zumkeller, Jan 04 2002

Keywords

• nonn

Comments

a(A000961(m)) = 1; a(A001358(m)) = A008472(A001358(m)).

Examples

			a(120) = 120/2^3 + 120/3^1 + 120/5^1 = 15 + 40 + 24 = 79.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, B8.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005236.

Cf. A028236. - R. J. Mathar, Sep 30 2008

Programs

Mathematica

f[n_ ] := n*Plus @@ (1/#[[1]]^#[[2]] & /@ FactorInteger@n); Array[f, 83] (* Robert G. Wilson v *)

PARI

{ for (n=1, 1000, f=factor(n); a=sum(i=1, matsize(f)[1], n/(f[i, 1]^f[i, 2])); write("b066504.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 18 2010

Extensions

More terms from Robert G. Wilson v, Dec 06 2005