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

Author

Amiram Eldar, Dec 25 2020

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Subsequence of A339979.

A307959 is a subsequence.

Similar sequence: A180332.

Programs

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]