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

1,6

Comments

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

References

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A005236.

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

Sequence in context: A340678 A028235 A028236 * A367202 A292771 A369364

Adjacent sequences: A066501 A066502 A066503 * A066505 A066506 A066507

Keyword

nonn

Author

Reinhard Zumkeller, Jan 04 2002

Extensions

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

Status

approved