A100390 -id:A100390 - cp's OEIS frontend

A082418 Numbers n such that P(n) > P(n+1) < P(n+2), where P(n) = largest prime factor of n (A006530).

3, 5, 7, 11, 15, 17, 19, 23, 26, 29, 31, 35, 39, 41, 44, 47, 49, 51, 53, 55, 59, 63, 65, 67, 69, 71, 74, 76, 80, 83, 87, 89, 95, 97, 99, 101, 104, 107, 109, 111, 113, 116, 119, 124, 127, 129, 131, 134, 137, 139, 143, 146, 149, 153, 155, 159, 161, 164, 167, 174, 179, 181, 183

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, A082417-A082422, A071869, A071870.

Flatten[Position[Partition[Table[FactorInteger[n][[-1,1]],{n,200}],3,1], ?(#[[1]]> #[[2]] <#[[3]]&),{1},Heads->False]] (* _Harvey P. Dale, Jan 10 2016 *)

a(n) = A100390(n) - 1. - T. D. Noe, Nov 26 2007

A100392 Numbers k such that A006530(k-1) < A006530(k) > A006530(k+1).

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 26, 29, 31, 34, 37, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 73, 76, 79, 83, 86, 89, 94, 97, 99, 101, 103, 107, 109, 111, 113, 116, 118, 122, 127, 129, 131, 134, 137, 139, 142, 146, 149, 151, 155, 157, 161, 163, 167, 173, 179

Offset: 1

Labos Elemer, Dec 14 2004

nonn

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

The sequence contains all odd primes.

			26 is here because the largest prime factors of 25, 26, 27 are 5, 13, 3.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A006530, A100390, A100393.

<?(First[#]<#[[2]]>Last[#]&),{1},Heads-> False]]+ 1] (* _Harvey P. Dale, Feb 22 2014 *)

a(n) = A082417(n) + 1. - T. D. Noe, Nov 26 2007

Edited by Don Reble, Jun 13 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

A100391 Prime powers which are local minima of A006530.

Original entry on oeis.org

4, 8, 16, 27, 32, 64, 81, 125, 128, 243, 256, 343, 512, 625, 729, 1024, 1331, 2048, 2187, 2197, 3125, 4096, 6561, 8192, 14641, 15625, 16384, 16807, 19683, 24389, 28561, 32768, 50653, 59049, 65536, 68921, 78125, 79507, 83521, 103823, 117649, 130321

Offset: 1

Labos Elemer, Dec 14 2004

nonn

			Largest prime factors around 49 are {3,7,5} so 49 is not a member.
k = 343 = 7^3 is in the sequence because the corresponding largest prime factors are {19,7,43}.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A006530, A100390.

N:= 2*10^5: # to get all terms <= N
f:= proc(x,p)
  if max(numtheory:-factorset(x-1))>p
    and max(numtheory:-factorset(x+1))>p  then x
    fi
end proc:
sort([seq(seq(f(p^i,p),i=2..floor(log[p](N))),p=select(isprime, [2,seq(i,i=3..floor(sqrt(N)),2)]))]); # Robert Israel, Jul 12 2018

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A082418 Numbers n such that P(n) > P(n+1) < P(n+2), where P(n) = largest prime factor of n (A006530).

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A100392 Numbers k such that A006530(k-1) < A006530(k) > A006530(k+1).

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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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A100391 Prime powers which are local minima of A006530.

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Maple

Mathematica