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A171453 a(n) = sum_i p_i^(e_i-1) where n = product_i p_i^e_i is the prime number decomposition of n.

%I A171453 #12 Jul 01 2024 10:41:57
%S A171453 0,1,1,2,1,2,1,4,3,2,1,3,1,2,2,8,1,4,1,3,2,2,1,5,5,2,9,3,1,3,1,16,2,2,
%T A171453 2,5,1,2,2,5,1,3,1,3,4,2,1,9,7,6,2,3,1,10,2,5,2,2,1,4,1,2,4,32,2,3,1,
%U A171453 3,2,3,1,7,1,2,6,3,2,3,1,9,27,2,1,4,2,2,2,5,1,5,2,3,2,2,2,17,1,8,4,7
%N A171453 a(n) = sum_i p_i^(e_i-1) where n = product_i p_i^e_i is the prime number decomposition of n.
%H A171453 Antti Karttunen, <a href="/A171453/b171453.txt">Table of n, a(n) for n = 1..10000</a>
%F A171453 a(n) = A008475(n) - A067240(n).
%p A171453 A171453 := proc(n) add( op(1,f)^(op(2,f)-1),f =ifactors(n)[2]) ; end proc:
%p A171453 seq(A171453(n),n=1..100) ;
%o A171453 (PARI) A171453(n) = { my(f=factor(n)); vecsum(vector(#f~,i,f[i,1]^(f[i,2]-1))); }; \\ _Antti Karttunen_, Sep 24 2017
%o A171453 (Python)
%o A171453 from sympy import factorint
%o A171453 def A171453(n): return sum(p**(e-1) for p,e in factorint(n).items()) # _Chai Wah Wu_, Jul 01 2024
%Y A171453 Cf. A008475, A067240.
%K A171453 easy,nonn
%O A171453 1,4
%A A171453 _R. J. Mathar_, Dec 09 2009