A100392 -id:A100392 - cp's OEIS frontend

A082417 Numbers k such that P(k) < P(k+1) > P(k+2), where P(k) is the largest prime factor of k (A006530).

2, 4, 6, 10, 12, 16, 18, 22, 25, 28, 30, 33, 36, 40, 42, 46, 48, 50, 52, 54, 58, 60, 64, 66, 68, 70, 72, 75, 78, 82, 85, 88, 93, 96, 98, 100, 102, 106, 108, 110, 112, 115, 117, 121, 126, 128, 130, 133, 136, 138, 141, 145, 148, 150, 154, 156, 160, 162, 166, 172, 178, 180, 182

Offset: 1

N. J. A. Sloane, Apr 25 2003

nonn

Antal Balog, On the largest prime factor of consecutive integers, Abstracts Amer. Math. Soc., 25 (No. 2, 2002), p. 337, #975-11-76.

T. D. Noe, Table of n, a(n) for n = 1..1000
P. Erdős and C. Pomerance, On the largest prime factors of n and n+1, Aequationes Math. 17 (1978), p. 311-321. [alternate link]

Cf. A006530, A082418-A082422, A071869, A071870, A100392.

gpf[n_] := FactorInteger[n][[-1, 1]]; ind = Position[Differences[Array[gpf, 200]], ?(# > 0 &)] // Flatten; ind[[Position[Differences[ind], ?(# > 1 &)] // Flatten]] (* Amiram Eldar, Jun 06 2022 *)

a(n) = A100392(n) - 1. - T. D. Noe, Nov 26 2007

A100393 Composite numbers k such that Gpf(k-1) < Gpf(k) > Gpf(k+1), where Gpf = A006530.

Original entry on oeis.org

26, 34, 49, 51, 55, 65, 69, 76, 86, 94, 99, 111, 116, 118, 122, 129, 134, 142, 146, 155, 161, 183, 185, 188, 202, 206, 209, 214, 218, 237, 244, 246, 249, 254, 265, 267, 274, 287, 291, 295, 298, 302, 305, 309, 321, 326, 329, 334, 339, 341, 344, 351, 356, 362

Offset: 1

Labos Elemer, Dec 14 2004

nonn

A006530(k) is the largest prime factor of k.

			26 is in the sequence because the largest prime factors of 25, 26, and 27 are 5, 13, and 3, respectively.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A006530, A100390, A100392.

gpf:= n -> max(numtheory:-factorset(n)):
L:= map(gpf, [$1..1000]):
select(t -> L[t]<> t and L[t]>L[t-1] and L[t]>L[t+1], [$2..nops(L)-1]); # Robert Israel, Jul 12 2018

<?(#[[1]]< #[[2]]> #[[3]]&),1,Heads->False]],CompositeQ[#+1]&]+1 (* _Harvey P. Dale, May 10 2022 *)

Edited by Don Reble, Jun 13 2007

cp's OEIS Frontend

A082417 Numbers k such that P(k) < P(k+1) > P(k+2), where P(k) is the largest prime factor of k (A006530).

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A100393 Composite numbers k such that Gpf(k-1) < Gpf(k) > Gpf(k+1), where Gpf = A006530.

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