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A379113 a(1) = 1; for n > 1, a(n) is the greatest proper unitary divisor d of n such that A048720(A065621(sigma(d)),sigma(n/d)) is equal to sigma(n).

%I A379113 #10 Dec 17 2024 18:30:23
%S A379113 1,1,1,1,1,3,1,1,1,5,1,3,1,7,3,1,1,1,1,5,7,11,1,3,1,2,1,7,1,15,1,1,3,
%T A379113 1,7,1,1,1,3,5,1,21,1,11,1,23,1,3,1,2,3,13,1,1,11,7,3,2,1,15,1,31,7,1,
%U A379113 5,33,1,1,3,35,1,9,1,1,3,19,7,6,1,5,1,1,1,21,1,43,3,11,1,1,7,23,31,47,1,3,1,1,1,4,1
%N A379113 a(1) = 1; for n > 1, a(n) is the greatest proper unitary divisor d of n such that A048720(A065621(sigma(d)),sigma(n/d)) is equal to sigma(n).
%H A379113 Antti Karttunen, <a href="/A379113/b379113.txt">Table of n, a(n) for n = 1..65537</a>
%H A379113 <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>.
%H A379113 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>.
%H A379113 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379113 a(n) = n/A379119(n).
%o A379113 (PARI)
%o A379113 A048720(b,c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
%o A379113 A065621(n) = bitxor(n-1,n+n-1);
%o A379113 A379113(n) = if(1==n,n,my(s=sigma(n)); fordiv(n,d,if((d>1) && 1==gcd(d,n/d) && A048720(A065621(sigma(n/d)),sigma(d))==s,return(n/d))));
%Y A379113 Cf. A000203, A048720, A065621, A379114 (positions of terms > 1), A379119.
%Y A379113 Cf. also A325567.
%K A379113 nonn
%O A379113 1,6
%A A379113 _Antti Karttunen_, Dec 17 2024