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%I #12 Oct 26 2023 05:20:41
%S 1,3,1,5,3,3,1,9,5,9,3,5,7,3,3,17,9,15,5,15,1,9,3,9,13,21,7,5,15,9,1,
%T 33,3,27,3,25,19,15,7,27,21,3,11,15,15,9,3,17,25,39,9,35,27,21,9,9,5,
%U 45,15,15,31,3,5,65,21,9,17,45,3,9,9,45,37,57,13,25,3,21,5,51,41,63,21,5,27
%N Odd part of sum of unitary divisors of n.
%C Since a(n) < n for any odd n > 1, iterating this function always leads to 1.
%H Antti Karttunen, <a href="/A161946/b161946.txt">Table of n, a(n) for n = 1..16384</a>
%F Multiplicative with a(p^e) = oddpart(p^e+1), where oddpart(n) = A000265(n) is the largest odd divisor of n.
%t Table[NestWhile[#/2 &, DivisorSum[n, # &, CoprimeQ[#, n/#] &], EvenQ@ # &], {n, 85}] (* _Michael De Vlieger_, Nov 23 2017 *)
%t a[n_] := Times @@ ((#/2^IntegerExponent[#, 2]) & /@ (1 + Power @@@ FactorInteger[n])); Array[a, 100] (* _Amiram Eldar_, Oct 26 2023 *)
%o (PARI) oddpart(n)=n/2^valuation(n,2)
%o a(n)=local(fm,r);fm=factor(n);r=1;for(k=1,matsize(fm)[1],r*=oddpart(fm[k,1]^fm[k,2]+1));r
%Y Cf. A000265, A161942, A034448, A151659.
%K easy,mult,nonn
%O 1,2
%A _Franklin T. Adams-Watters_, Jun 22 2009
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