A339981 Primitive coreful Zumkeller numbers: coreful Zumkeller numbers (A339979) having no coreful Zumkeller aliquot divisor.

36, 200, 392, 1936, 2704, 4900, 9248, 11552, 16928, 26912, 30752, 60500, 84500, 87616, 99225, 107584, 118336, 141376, 163592, 165375, 179776, 222784, 231525, 238144, 349448, 574592, 645248, 682112, 798848, 881792, 1013888, 1204352, 1225125, 1305728, 1357952

Offset

1,1

Comments

If m is a coreful Zumkeller number and k is a squarefree number such that gcd(m, k) = 1, then k*m is also a coreful Zumkeller number.

Links

Table of n, a(n) for n=1..35.

Example

a(1) = 36 since it is the least coreful Zumkeller number.
The next coreful Zumkeller numbers, 72, 144 and 180, are not terms since they are multiples of 36.

Mathematica

corZumQ[n_] := corZumQ[n] = Module[{r = Times @@ FactorInteger[n][[;; , 1]], d, sum, x}, d = r*Divisors[n/r]; (sum = Plus @@ d) >= 2*n && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]; primczQ[n_] := corZumQ[n] && NoneTrue[Most @ Divisors[n], corZumQ]; Select[Range[10^6], primczQ]

Crossrefs

Subsequence of A339979.

A307959 is a subsequence.

Similar sequence: A180332.

Sequence in context: A211764 A255093 A017138 * A304378 A120465 A361209

Adjacent sequences: A339978 A339979 A339980 * A339982 A339983 A339984

Keyword

nonn

Author

Amiram Eldar, Dec 25 2020

Status

approved