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URL: https://oeis.org/A176070

⇱ A176070 - OEIS

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A176070
Numbers of the form k^3+k^2+k+1 that are the product of two distinct primes.
2
15, 85, 259, 1111, 4369, 47989, 65641, 291919, 2016379, 2214031, 3397651, 3820909, 5864581, 9305311, 13881841, 15687751, 16843009, 19756171, 22030681, 28746559, 62256349, 64160401, 74264821, 79692331, 101412319, 117889591, 172189309, 185518471, 191435329, 270004099, 328985791
OFFSET
1,1
COMMENTS
As k^3 + k^2 + k + 1 = (k + 1) * (k^2 + 1) and k <= 1 does not give a term, k + 1 and k^2 + 1 must be prime so k must be even. - David A. Corneth, May 30 2023
FORMULA
a(n) = (A070689(n + 1) + 1) * (A070689(n + 1)^2 + 1). - David A. Corneth, May 30 2023
EXAMPLE
15 is in the sequence as 15 = 3*5 = 2^3+2^2+2+1; 15 is a product of two distinct primes and of the form k^3 + k^2 + k + 1.
MATHEMATICA
f[n_]:=Last/@FactorInteger[n]=={1, 1}; Select[Array[ #^3+#^2+#+1&, 7! ], f[ # ]&]
PROG
(PARI) upto(n) = {my(res = List(), u = sqrtnint(n, 3) + 1); forprime(p = 3, u, c = (p-1)^2 + 1; if(isprime(c), listput(res, c*p))); res} \\ David A. Corneth, May 30 2023
CROSSREFS
Cf. A002496, A006093, A006881, A053698, A070689, A174969, A176069, A237627 (semiprimes of that form).
Sequence in context: A206169 A160599 A091286 * A160747 A064058 A138322
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name corrected by and more terms from David A. Corneth, May 30 2023
STATUS
approved