A379113 - OEIS

%I #10 Dec 17 2024 18:30:23

%S 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 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 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 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 Antti Karttunen, <a href="/A379113/b379113.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>.

%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F a(n) = n/A379119(n).

%o (PARI)

%o A048720(b,c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);

%o A065621(n) = bitxor(n-1,n+n-1);

%o 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 Cf. A000203, A048720, A065621, A379114 (positions of terms > 1), A379119.

%Y Cf. also A325567.

%K nonn,new

%O 1,6

%A _Antti Karttunen_, Dec 17 2024