A360561 a(n) is the least multiple of n that is a Zumkeller number (A083207).

6, 6, 6, 12, 20, 6, 28, 24, 54, 20, 66, 12, 78, 28, 30, 48, 102, 54, 114, 20, 42, 66, 138, 24, 150, 78, 54, 28, 174, 30, 186, 96, 66, 102, 70, 108, 222, 114, 78, 40, 246, 42, 258, 88, 90, 138, 282, 48, 294, 150, 102, 104, 318, 54, 220, 56, 114, 174, 354, 60

Offset: 1

Author

Rémy Sigrist, Feb 11 2023

Keywords

• nonn

Comments

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.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• K. P. S. Bhaskara Rao and Yuejian Peng, On Zumkeller Numbers, arXiv:0912.0052 [math.NT], 2009.

Crossrefs

Cf. A083207, A360562.

Programs

PARI

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

Formula

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

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