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