A360561 - OEIS

%I #13 Feb 14 2023 12:54:49

%S 6,6,6,12,20,6,28,24,54,20,66,12,78,28,30,48,102,54,114,20,42,66,138,

%T 24,150,78,54,28,174,30,186,96,66,102,70,108,222,114,78,40,246,42,258,

%U 88,90,138,282,48,294,150,102,104,318,54,220,56,114,174,354,60

%N a(n) is the least multiple of n that is a Zumkeller number (A083207).

%C This sequence is well defined: as stated in Rao and Peng: 6 = 2*3 is a Zumkeller number, so, for any u, v >= 0, 2^(1+2*u) * 3^(1+2*v) is a Zumkeller number, also, if z is a Zumkeller number and m is coprime to z then z*m is also a Zumkeller number; if n = 2^u * 3^v * m with m coprime to 6, let u' be the least odd number >= u and v' be the least odd number >= v, then k = 2^(u'-u) * 3^(v'-v) is an integer (among {1, 2, 3, 6}), k*n is a Zumkeller number and a(n) <= k.

%H Rémy Sigrist, <a href="/A360561/b360561.txt">Table of n, a(n) for n = 1..10000</a>

%H K. P. S. Bhaskara Rao and Yuejian Peng, <a href="http://arxiv.org/abs/0912.0052">On Zumkeller Numbers</a>, arXiv:0912.0052 [math.NT], 2009.

%F a(n) = A360562(n) * n.

%F a(n) = n iff n belongs to A083207.

%o (PARI) a(n) = { forstep (m=n, oo, n, if (is(m), return (m))) } \\ see A083207 for the function "is"

%Y Cf. A083207, A360562.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Feb 11 2023