A087429 -id:A087429 - cp's OEIS frontend

A137222 Partial sums of A087429.

1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 18, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 23, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 31, 32, 32, 33, 33, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 38, 39

Offset: 1

Giovanni Teofilatto, Mar 07 2008

Cf. A087429.

A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc: A087429 := proc(n) if A006530(n+1) > A006530(n) then 1 ; else 0 ; end if; end proc: A137222 := proc(n) add( A087429(j),j=1..n) ; end proc: seq(A137222(n),n=1..100) ; # R. J. Mathar, Jan 30 2010

Terms beyond a(18) from R. J. Mathar, Jan 30 2010

A087430 Nonprimes n with gpf(n) > gpf(n+1), where gpf=A006530 (greatest prime factor).

Original entry on oeis.org

14, 15, 26, 34, 35, 38, 39, 44, 49, 51, 55, 62, 63, 65, 69, 74, 76, 80, 86, 87, 94, 95, 99, 104, 111, 116, 118, 119, 122, 123, 124, 129, 134, 142, 143, 146, 152, 153, 155, 158, 159, 161, 164, 174, 183, 185, 186, 188, 194, 195, 202, 203, 206, 207, 209, 214, 215

Offset: 1

Reinhard Zumkeller, Sep 02 2003

nonn

Subsequence of A070087.

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

Cf. A087429.

N:= 1000: # to get all terms < N
V:= Vector(N):
p:= 1:
do
  p:= nextprime(p);
  if p > N then break fi;
  V[[seq(k*p,k=1..N/p)]]:= p
od:
select(t -> V[t] > V[t+1] and not isprime(t), [$1..N-1]); # Robert Israel, Jul 03 2018

With[{nn=250},Select[Complement[Range[nn],Prime[Range[PrimePi[ nn]]]], FactorInteger[ #][[-1,1]]>FactorInteger[#+1][[-1,1]]&]] (* Harvey P. Dale, Jul 14 2016 *)

A359953 a(1) = 0, a(2) = 1. For n >= 3, if the greatest prime dividing n is greater than the greatest prime dividing n-1, then a(n) = a(n-1) + 1. Otherwise a(n) = a(n-1) - 1.

Original entry on oeis.org

0, 1, 2, 1, 2, 1, 2, 1, 2, 3, 4, 3, 4, 3, 2, 1, 2, 1, 2, 1, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 6, 7, 6, 5, 6, 5, 4, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 5, 6, 5, 6, 5, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3

Offset: 1

Tamas Sandor Nagy, Jan 19 2023

The first negative value is at a(3888). Within the first 1000000 values are the negative record values a(n) = -4 at n = {3913, 3915, 3927, 3933}. - Thomas Scheuerle, Jan 20 2023

			a(5) = a(4) + 1 = 1 + 1 = 2 because A006530(5) = 5 > A006530(4) = 2.

Cf. A000040, A006530, A070089, A087429.

function a = A359953(max_n)
    a = [0 cumsum(sign(diff([0 arrayfun(@(x)(max(factor(x))),[2:max_n])])))];
end % Thomas Scheuerle, Jan 20 2023

Join[{0}, Accumulate@ Sign@ Differences@ Table[FactorInteger[n][[-1, 1]], {n, 1, 100}]] (* Amiram Eldar, Jan 20 2023, after the MATLAB code *)

lista(nn) = my(va = vector(nn)); va[1] = 0; va[2] = 1; for (n=3, nn, if (vecmax(factor(n)[,1]) > vecmax(factor(n-1)[,1]), va[n] = va[n-1] + 1, va[n] = va[n-1] - 1);); va; \\ Michel Marcus, Jan 31 2023

For n >= 2, if A006530(n) > A006530(n-1), then a(n) = a(n-1) + 1; a(n) = a(n-1) - 1 otherwise.
a(n) = (-1)*Sum_{i=1..n-1} (-1)^A087429(i).
a(1 + A070089(n)) = 1 + a(A070089(n)). - Thomas Scheuerle, Jan 20 2023

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A137222 Partial sums of A087429.

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A087430 Nonprimes n with gpf(n) > gpf(n+1), where gpf=A006530 (greatest prime factor).

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A359953 a(1) = 0, a(2) = 1. For n >= 3, if the greatest prime dividing n is greater than the greatest prime dividing n-1, then a(n) = a(n-1) + 1. Otherwise a(n) = a(n-1) - 1.

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