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 A175143 a(1)=1. a(n) = the smallest integer > a(n-1) such that d(a(n))+d(a(n)+1) > d(a(n-1))+d(a(n-1)+1), where d(m) = the number of divisors of m. 4
 1, 2, 3, 5, 8, 11, 15, 20, 24, 35, 59, 80, 84, 119, 224, 239, 335, 359, 360, 480, 539, 719, 720, 840, 1079, 1259, 1260, 1679, 2519, 4199, 5039, 5040, 6720, 7559, 9360, 10079, 10080, 15119, 20159, 25199, 25200, 27719, 32759, 43680, 50399, 55439, 75599 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Those n where A092405(n) sets records. Nicolas proved that: (1) Except for a finite number of terms, if k is in this sequence either k or k+1 is a largely composite number (A067128). (2) Except for a finite number of terms if k is a highly composite number (A002182) then k-1 is a term of this sequence. Apparently the only exceptions of (1) are 15, 80, 224, 6720, and 9360, and the only exceptions of (2) are 1, 24, 48, 180, 840, and 45360. - Amiram Eldar, Aug 24 2019 LINKS Amiram Eldar, Table of n, a(n) for n = 1..145 Jean-Louis Nicolas, Nombres hautement composés, Acta Arithmetica, Vol. 49 (1988), pp. 395-412, alternative link. See p. 398. MAPLE A092405 := proc(n) numtheory[tau](n)+numtheory[tau](n+1) ; end proc: read("transforms") ; a092405 :=[seq(A092405(n), n=1..90000)] ; RECORDS(a092405)[2] ; # R. J. Mathar, Mar 05 2010 MATHEMATICA d1 = 1; dm = 0; s = {}; Do[d2 = DivisorSigma[0, n]; d = d1 + d2; If[d > dm, dm = d; AppendTo[s, n - 1]]; d1 = d2, {n, 2, 80000}]; s (* Amiram Eldar, Aug 24 2019 *) smi[n_]:=Module[{k=n+1, ds=DivisorSigma[0, n]+DivisorSigma[0, n+1]}, While[ DivisorSigma[ 0, k]+DivisorSigma[0, k+1]<=ds, k++]; k]; NestList[smi, 1, 50] (* Harvey P. Dale, Apr 25 2020 *) CROSSREFS Cf. A000005, A002182, A067128, A092405. Sequence in context: A024611 A131073 A062485 * A137179 A356549 A096777 Adjacent sequences: A175140 A175141 A175142 * A175144 A175145 A175146 KEYWORD nonn AUTHOR Leroy Quet, Feb 24 2010 EXTENSIONS Extended by Ray Chandler, Mar 05 2010 Terms beyond 80 from R. J. Mathar, Mar 05 2010 STATUS approved

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Last modified September 11 15:45 EDT 2024. Contains 375836 sequences. (Running on oeis4.)