A190136 Largest prime factor of n*(n+1)*(n+2)*(n+3).
3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 13, 13, 29, 29, 31, 31, 31, 31, 17, 17, 37, 37, 37, 37, 41, 41, 43, 43, 43, 43, 47, 47, 47, 47, 17, 17, 53, 53, 53, 53, 19, 29, 59, 59, 61, 61, 61, 61, 31, 13, 67, 67, 67
Offset: 1
Keywords
Examples
Numbers m <= 10^6 such that a(m) = p: p=13: 10, 11, 12, 13, 24, 25, 63; p=17: 14, 15, 32, 33, 48, 49; p=19: 16, 17, 18, 19, 54, 75, 168; p=23: 20, 21, 22, 23, 207, 322; p=29: 26, 27, 55, 114; p=31: 28, 29, 30, 31, 62, 90, 152, 153, 340, 493, 1518; p=37: 34, 35, 36, 37, 74, 184, 405; p=41: 38, 39, 123, 245, 285, 286, 287, 492, 1023, 1517, 1680; p=43: 40, 41, 42, 43, 84, 85, 169, 258, 341, 342, 558, 1330, 1331, 2106, 5289, 10878; p=47: 44, 45, 46, 47, 91, 92, 93, 185, 186, 187, 374, 375, 702, 986, 987, 17575; p=53: 50, 51, 52, 53, 159, 368, 369, 527, 845, 899, 900, 1375; p=59: 56, 57, 115, 116, 117, 118, 174, 294, 528, 529, 530, 648, 943, 1885, 6783; p=61: 58, 59, 60, 61, 119, 120, 121, 122, 182, 183, 242, 243, 244, 549, 608, 609, 1034, 1218, 1219, 1767, 1768, 2013, 2254, 2622; p=67: 64, 65, 66, 67, 132, 133, 735, 1271, 1272, 1273, 2208, 2277, 3885, 4958, 5828, 5829; p=71: 68, 69, 140, 141, 142, 284, 423, 424, 494, 636, 637, 779, 780, 781, 3477, 3478, 3549, 3550, 4899; p=73: 70, 71, 72, 73, 143, 144, 145, 219, 363, 510, 728, 729, 803, 1022, 1239, 1679, 2772, 70224; p=79: 76, 77, 78, 79, 158, 234, 235, 472, 473, 474, 550, 867, 868, 1024, 1104, 1419, 2209, 2448, 2923, 3476, 3869, 4898, 5290, 7502, 46136, 70150; p=83: 80, 81, 82, 83, 246, 247, 413, 495, 663, 664, 1078, 1159, 1824, 2736, 3483, 4232, 4896, 4897, 7137, 8214, 12614, 36517, 97524; p=89: 86, 87, 88, 89, 175, 264, 265, 354, 531, 710, 711, 712, 798, 1245, 1332, 2847, 4895, 5073, 6318, 18423, 28302, 29279; p=97: 94, 95, 96, 97, 288, 289, 483, 580, 581, 582, 774, 873, 1064, 1065, 1455, 2132, 2133, 3007, 3975, 4556, 4557, 6496, 6497, 6887, 7564, 7565, 7566, 13869, 17457.
References
- Paulo Ribenboim, Galimatias Arithmeticae (Chap 11), in 'My Numbers, My Friends', Springer-Verlag 2000 NY, page 345.
- J. J. Sylvester, "On arithmetical series", Messenger of Mathematics 21 (1892), pp. 1-19 and 87-120.
- M. Faulkner, "On a theorem of Sylvester and Schur", J. London Math. Soc. 41:1 (1966), pp. 107-110.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- Eric Weisstein's World of Mathematics, Greatest Prime Factor
Programs
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Haskell
a190136 n = maximum $ map a006530 [n..n+3]
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Mathematica
Table[FactorInteger[Times@@(n+Range[0,3])][[-1,1]],{n,70}] (* Harvey P. Dale, Mar 19 2018 *) -
PARI
gpf(n)=vecmax(factor(n)[,1]) a(n)=my(p=precprime(n+3));if(p
Formula
a(n) = max{gpf(n), gpf(n+1), gpf(n+2), gpf(n+3)} = gpf(A052762(n+3)) with gpf = A006530, greatest prime factor.
a(n) > 47 for n > 17575. - Charles R Greathouse IV, Feb 19 2013
Comments