A036097 -id:A036097 - cp's OEIS frontend

A036098 Centered cube numbers: a(n) = (n+1)^20 + n^20.

1, 1048577, 3487832977, 1102998412177, 96466943268401, 3751525871703601, 83448424737674977, 1232713770904458977, 13310586963663775777, 112157665459056928801, 772749994932560009201, 4506509987380035131377

Offset: 0

N. J. A. Sloane

Never prime because a(n) = (2n^4 + 4n^3 + 6n^2 + 4n + 1) * (n^16 + 8n^15 + 76n^14 + 392n^13 + 1394n^12 + 3632n^11 + 7112n^10 + 10656n^9 + 12376n^8 + 11220n^7 + 7942n^6 + 4356n^5 + 1819n^4 + 560n^3 + 120n^2 + 16n + 1). Semiprime for n in {1, 13, 14, 54, 162, ...}. - Jonathan Vos Post, Aug 27 2011

			a(1) = 1^20 + (1+1)^20 = 1048577 = 17 * 61681, which is semiprime.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Cf. A010808, A036096, A036097.

[(n+1)^20+n^20: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

A036099 Centered cube numbers: (n+1)^21 + n^21.

Original entry on oeis.org

1, 2097153, 10462450355, 4408506864307, 481235204714229, 22413787798580981, 580482814723661863, 9781917900938059815, 118642361168367135017, 1109418989131512359209, 8400249944258160101211, 53405369853627861567323

Offset: 0

N. J. A. Sloane

After a(0) always has at least 4 prime factors, because a(n) = (2n + 1) * (n^2 + n + 1) * (n^6 + 3n^5 + 9n^4 + 13n^3 + 11n^2 + 5n + 1) * (n^12 + 6n^11 + 63n^10 + 260n^9 + 643n^8 + 1078n^7 + 1275n^6 + 1078n^5 + 650n^4 + 274n^3 + 77n^2 + 13n + 1). [Jonathan Vos Post, Aug 27 2011]

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A010809, A036098, A036097.

[(n+1)^21+n^21: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

Total/@Partition[Range[0,20]^21,2,1] (* Harvey P. Dale, Jul 02 2019 *)

cp's OEIS Frontend

A036098 Centered cube numbers: a(n) = (n+1)^20 + n^20.

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