A344595 Numbers k such that A011772(k) > A344878(k) and A011772(k) is a divisor of A344875(k).

900, 1260, 1302, 1560, 2100, 3906, 4440, 6300, 6552, 6669, 9680, 11544, 12987, 15368, 18981, 19240, 19880, 24120, 26208, 35784, 36080, 42680, 46104, 57720, 59040, 59640, 62238, 62244, 71136, 74592, 76840, 79376, 81872, 84700, 101680, 103730, 108500, 124488, 128040, 145188, 160160, 168020, 171740, 178920, 185724, 201608

Offset: 1

Author

Antti Karttunen, Jun 05 2021

Keywords

• nonn

Comments

Numbers k for which A344973(k) = 0 and A344976(k) < 0.

It seems that in these cases, by necessity A011772(k) < A344875(k), i.e., A011772(k) is a proper divisor of A344875(k).

Has many terms common with A344694.

Crossrefs

Cf. A011772, A344694, A344875, A344878, A344973, A344976.

Intersection of A024619, A344974 and A344977.

Intersection of A344975 and A344977.

Programs

PARI

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
A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
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))));
isA344595(n) = { my(u=A011772(n)); (u>A344878(n)&&0==(A344875(n)%u)); };