A080371 a(n) is the smallest x such that the quotient d(x+1)/d(x) equals n, where d = A000005.

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

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