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A180082 Semiprime centered cube numbers: m^3 + (m+1)^3. 2
9, 35, 91, 341, 559, 1241, 6119, 7471, 17261, 19909, 75241, 143009, 257651, 323839, 671509, 860851, 967591, 1433969, 1482571, 1970299, 2348641, 2772559, 3413159, 4548059, 5313691, 5666509, 7233841, 7520291, 9568441 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are no prime centered cube numbers, n^3 + (n+1)^3, as Howard Berman proves in a comment to A005898. 0^3 + (0+1)^3 = 1, which has Omega(1) A001222(1) = 0 by convention.  Hence MINIMUM[n>0] Omega(a(n^3 + (n+1)^3)) = 2, which occurs for the values of this sequence.

There are no prime centered cube numbers because m^3+(m+1)^3=(2m+1)(m^2+m+1). - Zak Seidov, Feb 08 2011

m=(1, 2, 3, 5, 6, 8, 14, 15, 20, 21, 33, 41, 50, 54, 69, 75, 78, 89, 90, 99, 105, 111, 119, 131, 138, 141, 153, 155, 168, 173, 176, 189, 194, 209, 215, 231, 245,...). - Vincenzo Librandi, Feb 06 2011

Products of two primes p and q=(p^2+3)/4 with p's in A118939. - Zak Seidov, Feb 08 2011

LINKS

Table of n, a(n) for n=1..29.

FORMULA

A001358 INTERSECTION A005898.

EXAMPLE

a(1) = 1^3 + (1+1)^3 = 9 = 3^2 is semiprime.

a(2) = 2^3 + (2+1)^3 = 35 = 5 * 7.

a(3) = 3^3 + (3+1)^3 = 91 = 7 * 13.

CROSSREFS

Cf. A001222, A001358, A005898.

Sequence in context: A212100 A005898 A034957 * A002418 A118414 A279218

Adjacent sequences:  A180079 A180080 A180081 * A180083 A180084 A180085

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Feb 06 2011

EXTENSIONS

More terms from Vincenzo Librandi, Feb 06 2011

STATUS

approved

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Last modified February 24 12:59 EST 2018. Contains 299623 sequences. (Running on oeis4.)