A344977 - OEIS

%I #12 Jun 05 2021 16:44:09

%S 14,15,30,33,35,38,42,45,51,56,62,63,65,69,70,84,85,86,87,88,90,91,99,

%T 102,104,105,114,115,116,117,123,126,130,133,134,135,141,143,145,152,

%U 153,154,158,159,161,165,168,170,172,174,175,177,180,182,185,186,195,200,204,206,210,213,215,217,221,225,234,235

%N Numbers k for which A011772(k) exceeds A344878(k).

%F {k such that A344976(k) < 0}.

%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 isA344977(n) = (A011772(n)>A344878(n));

%Y Cf. A011772, A344878.

%Y Positions of negative terms in A344976.

%Y Cf. A344595 (subsequence).

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 04 2021