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Numbers k such that A011772(k) is equal to A344878(k).
3

%I #6 Jun 05 2021 16:44:24

%S 1,2,3,4,5,7,8,9,11,13,16,17,19,21,23,25,26,27,29,31,32,37,39,41,43,

%T 47,49,50,53,57,59,61,64,67,71,73,74,75,78,79,81,83,89,93,97,98,101,

%U 103,107,109,111,113,121,122,125,127,128,129,131,137,139,146,147,149,150,151,157,163,167,169,173,179,181,183,191,193,194

%N Numbers k such that A011772(k) is equal to A344878(k).

%o (PARI)

%o A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772

%o A344878(n) = if(1==n,n, my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]^(f[2, i]+(2==f[1, i]))-1))));

%o isA344979(n) = (A344878(n)==A011772(n));

%Y Cf. A011772, A344878, A344885 (characteristic function).

%Y Positions of zeros in A344976.

%Y Union of A000961 and A344978. Subsequence of A344974.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 05 2021