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 A189882 Smallest k such that sopf(k)<=sopf(k+1)<=...<=sopf(k+n). 1
 1, 1, 4, 90, 714, 9352, 16575, 617139, 721970, 6449639, 1303324906, 13250660627, 37151747513, 211221121752 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 20 03:37 EDT 2022. Contains 353851 sequences. (Running on oeis4.)