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A379119 a(1) = 1; for n > 1, a(n) is the smallest unitary divisor d > 1 of n such that A048720(A065621(sigma(n/d)),sigma(d)) is equal to sigma(n).

%I A379119 #10 Dec 17 2024 19:35:30
%S A379119 1,2,3,4,5,2,7,8,9,2,11,4,13,2,5,16,17,18,19,4,3,2,23,8,25,13,27,4,29,
%T A379119 2,31,32,11,34,5,36,37,38,13,8,41,2,43,4,45,2,47,16,49,25,17,4,53,54,
%U A379119 5,8,19,29,59,4,61,2,9,64,13,2,67,68,23,2,71,8,73,74,25,4,11,13,79,16,81,82,83,4,85,2,29,8,89
%N A379119 a(1) = 1; for n > 1, a(n) is the smallest unitary divisor d > 1 of n such that A048720(A065621(sigma(n/d)),sigma(d)) is equal to sigma(n).
%H A379119 Antti Karttunen, <a href="/A379119/b379119.txt">Table of n, a(n) for n = 1..65537</a>
%H A379119 <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>.
%H A379119 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>.
%H A379119 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379119 a(n) = n / A379113(n).
%o A379119 (PARI)
%o A379119 A048720(b,c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
%o A379119 A065621(n) = bitxor(n-1,n+n-1);
%o A379119 A379119(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(d))));
%Y A379119 Cf. A000203, A048720, A065621, A379113, A379114 (positions of terms such that a(n) < n).
%Y A379119 Cf. also A379120.
%K A379119 nonn
%O A379119 1,2
%A A379119 _Antti Karttunen_, Dec 17 2024