A096176 -id:A096176 - cp's OEIS frontend

A096175 Numbers k such that k^3-1 is an odd semiprime.

6, 8, 12, 14, 20, 24, 38, 54, 62, 80, 90, 110, 138, 150, 164, 168, 192, 194, 272, 278, 314, 332, 348, 398, 402, 434, 500, 572, 642, 644, 720, 728, 762, 798, 812, 860, 864, 878, 920, 992, 1020, 1022, 1070, 1092, 1098, 1118, 1130, 1182, 1202, 1230, 1260, 1308

Offset: 1

Hugo Pfoertner, Jun 22 2004

nonn

			a(1)=6 because 6^3 - 1 = 216 - 1 = 215 = 5*43.

Hugo Pfoertner, Table of n, a(n) for n = 1..10000
Dario A. Alpern, Factorization using the Elliptic Curve Method

Cf. A096173: k^3+1 is an odd semiprime; A081257: largest prime factor of k^3-1; A096176 (k^3-1)/(k-1) is prime; A046315.

forstep (k=2,1310,2,if(bigomega(k^3-1)==2,print1(k,", ")))
\\ Hugo Pfoertner, Nov 28 2017

A081257 a(n) is the greatest prime factor of (n^3 - 1).

Original entry on oeis.org

7, 13, 7, 31, 43, 19, 73, 13, 37, 19, 157, 61, 211, 241, 13, 307, 17, 127, 421, 463, 13, 79, 601, 31, 37, 757, 271, 67, 29, 331, 151, 1123, 397, 97, 43, 67, 1483, 223, 547, 1723, 139, 631, 283, 109, 103, 61, 181, 43, 2551, 379, 919, 409, 2971, 79, 103, 3307, 163

Offset: 2

Jan Fricke, Mar 14 2003

The record values here (as well as those for A081256) appear to match the terms of A002383 for n > 1. - Bill McEachen, Jun 19 2023

			a(7)=19 because 7^3 - 1 = 342 = 2*3*3*19.

Jon E. Schoenfield, Table of n, a(n) for n = 2..10000 (first 999 terms from R. J. Mathar).

Cf. A081256, A081258, A002383.

Cf. A096175 (n^3-1 is an odd semiprime), A096176 ((n^3-1)/(n-1) is prime).

A081257 := proc(n)
        A006530( n^3-1) ;
end proc: # R. J. Mathar, Jul 18 2015

FactorInteger[#][[-1,1]]&/@(Range[2,60]^3-1) (* Harvey P. Dale, Oct 09 2017 *)

a(n)=my(f=factor(n^3-1)); f[#f~,1] \\ Charles R Greathouse IV, Mar 08 2017

from sympy import primefactors
def A081257(n): return max(primefactors(n-1)+primefactors(n*(n+1)+1)) # Chai Wah Wu, Oct 15 2022

a(n) = A006530(A068601(n)). - Michel Marcus, Jun 19 2023

More terms from Hugo Pfoertner, Jun 21 2004

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A096175 Numbers k such that k^3-1 is an odd semiprime.

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A081257 a(n) is the greatest prime factor of (n^3 - 1).

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