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 A080371 a(n) is the smallest x such that the quotient d(x+1)/d(x) equals n, where d = A000005. 5
 2, 1, 11, 23, 47, 59, 191, 167, 179, 239, 5119, 359, 20479, 2111, 719, 839, 983039, 1259, 786431, 3023, 2879, 15359, 62914559, 3359, 22031, 266239, 6299, 6719, 13690208255, 5039, 22548578303, 7559, 156671, 6881279, 25919, 10079, 1168231104511, 5505023, 479231, 21839 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(37) > 10^12. - Donovan Johnson, Sep 02 2013 Conjecture: a(p) = 2^(p-1) * k - 1 for some k > 0 and prime p. - David A. Corneth, Jan 26 2021 LINKS David A. Corneth, Table of n, a(n) for n = 1..196 Donovan Johnson, All 435 terms <= 10^12 FORMULA a(n) = Min_{x : d[x+1]/d[x] = n}. a(n) = A086551(n) - 1. - Hugo Pfoertner, Jan 26 2021 EXAMPLE n = 49: a(49) = 233279 = m, d(m+1) = 98, d(m) = 2, quotient = 49. MATHEMATICA t = Table[ 0, {50}]; Do[ s = DivisorSigma[0, n+1] / DivisorSigma[0, n]; If[ s < 51 && t[[s]] == 0, t[[s]] = n], {n, 1, 10^8}]; t PROG (PARI) {a(n) = my(k=1); while(numdiv(k+1)!=n*numdiv(k), k++); k} \\ Seiichi Manyama, Jan 17 2021 CROSSREFS Cf. A000005, A080372. Sequence in context: A305877 A111724 A184299 * A151337 A013019 A012904 Adjacent sequences:  A080368 A080369 A080370 * A080372 A080373 A080374 KEYWORD nonn AUTHOR Labos Elemer, Feb 24 2003 EXTENSIONS More terms from Robert G. Wilson v, Feb 27 2003 a(29) and a(31) from Donovan Johnson, Dec 26 2012 More terms from David A. Corneth, Jan 27 2021 STATUS approved

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Last modified April 13 02:47 EDT 2021. Contains 342934 sequences. (Running on oeis4.)