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A222416 If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 1 by convention). 7

%I

%S 1,2,3,4,5,5,7,8,9,7,11,7,13,9,8,16,17,11,19,9,10,13,23,11,25,15,27,

%T 11,29,10,31,32,14,19,12,13,37,21,16,13,41,12,43,15,14,25,47,19,49,27,

%U 20,17,53,29,16,15,22,31,59,12,61,33,16,64,18,16,67,21,26,14,71,17,73

%N If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 1 by convention).

%C A variant of A008475, which is the main entry.

%H Antti Karttunen, <a href="/A222416/b222416.txt">Table of n, a(n) for n = 1..16384</a>

%H Nussbaum, Roger D.; Verduyn Lunel, Sjoerd M., <a href="http://www.math.rutgers.edu/~nussbaum/Pubs/nusslunel2003.pdf">Asymptotic estimates for the periods of periodic points of non-expansive maps</a>, Ergodic Theory Dynam. Systems 23 (2003), no. 4, 1199--1226. See the function S(n). MR1997973 (2004m:37033)

%t Array[Total[Power @@@ FactorInteger[#]] &, 73] (* _Michael De Vlieger_, Nov 17 2017 *)

%o (PARI)

%o A008475(n) = { my(f=factor(n)); vecsum(vector(#f~,i,f[i,1]^f[i,2])); };

%o A222416(n) = if(1==n,n,A008475(n)); \\ _Antti Karttunen_, Nov 17 2017

%Y Cf. A008475, A222415.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Feb 28 2013

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Last modified May 30 22:27 EDT 2020. Contains 334747 sequences. (Running on oeis4.)