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

1,1

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.

Formula

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

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

Prog

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

Crossrefs

Cf. A083207, A360562.

Sequence in context: A315829 A180604 A254572 * A109047 A337814 A153171

Adjacent sequences: A360558 A360559 A360560 * A360562 A360563 A360564

Keyword

nonn

Author

Rémy Sigrist, Feb 11 2023

Status

approved