A189882 Smallest k such that sopf(k)<=sopf(k+1)<=...<=sopf(k+n).

1, 1, 4, 90, 714, 9352, 16575, 617139, 721970, 6449639, 1303324906, 13250660627, 37151747513, 211221121752

Offset

1,3

Comments

Sopf(k) is the sum of the distinct primes dividing k (A008472).

a(15) > 10^13. - Giovanni Resta, May 04 2017

Links

Table of n, a(n) for n=1..14.

Example

a(1) = 1 because sopf(1) < = sopf(2) => 0 < 2 ;
a(2) = 1 because sopf(1) <= sopf(2) <= sopf(3) => 0 < 2 < 3 ;
a(3) = 4 because sopf(4) <= sopf(5) <= sopf(6) <= sopf(7) => 2 < 5 <= 5 < 7 ;
a(4) = 90 because sopf(90) <= sopf(91) <= sopf(92) <= sopf(93) <= sopf(94) =>
  10 < 20 < 25 < 34 < 49.

Maple

with(numtheory):for n from 1 to 12 do: id:=0:for k0 from 2 to 20000 while(id=0)
  do:t:=0:for k from 0 to n-1 do: x1:=factorset(k0+k):x2:=factorset(k0+k+1):n1:=nops(x1):
  n2:=nops(x2):s1:=0:s2:=0:for p from 1 to n1 do:s1:=s1+x1[p]:od:for q from 1
  to n2 do:s2:=s2+x2[q]:od:if s1 <= s2 then t:=t+1:else fi:od:if t=n then id:=1:print(k0):else
  fi:od:od:

Mathematica

sopf[n_] := If[n == 1, 0, Total[First /@ FactorInteger@n]]; s = Array[sopf, 700000]; Table[ SelectFirst[Range[Length@s - n], Sort[t = Take[s, {#, # + n}]] == t &], {n, 8}] (* Giovanni Resta, May 04 2017 *)

Crossrefs

Cf. A008472, A286190.

Sequence in context: A292304 A337081 A218385 * A067767 A240379 A304190

Adjacent sequences: A189879 A189880 A189881 * A189883 A189884 A189885

Keyword

nonn,more

Author

Michel Lagneau, May 03 2011

Extensions

a(1)-a(2) corrected and a(12)-a(14) from Giovanni Resta, May 04 2017

Status

approved