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 A066504 Sum of n/p^k over all maximal prime-power divisors of n. 4

%I

%S 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,

%T 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,

%U 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

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

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

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

%H Harry J. Smith, <a href="/A066504/b066504.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%o (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

%Y Cf. A005236.

%Y Cf. A028236. - _R. J. Mathar_, Sep 30 2008

%K nonn

%O 1,6

%A _Reinhard Zumkeller_, Jan 04 2002

%E More terms from _Robert G. Wilson v_, Dec 06 2005

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)