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A253535 Lesser member of a harmonious pair. 2
4, 6, 14, 10, 20, 8, 15, 26, 60, 2, 42, 14, 66, 88, 102, 45, 10, 4, 174, 153, 164, 38, 15, 22, 220, 182, 110, 9, 92, 33, 345, 190, 6, 28, 285, 195, 435, 68, 78, 364, 315, 207, 2, 368, 248, 42, 51, 846, 790, 21, 870, 32, 334, 558, 82, 34, 117, 1184, 598, 574 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let sigma be the usual sum-of-divisors function. We say that x and y form a harmonious pair if x/sigma(x) + y/sigma(y) = 1. Equivalently, the harmonic mean of sigma(x)/x and sigma(y)/y is 2.

An amicable pair forms a harmonious pair, so the lesser member of an amicable pair A002025 is a term of this sequence.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000

Jamie Bishop, Abigail Bozarth, Rebekah Kuss, and Benjamin Peet, The Abundancy Index and Feebly Amicable Numbers, arXiv:2104.11366 [math.NT], 2021.

M. Kozek, F. Luca, P. Pollack, and C. Pomerance, Harmonious numbers, IJNT, to appear.

EXAMPLE

4 and 12 form a harmonious pair since 4/sigma(4) + 12/sigma(12) = 4/7 + 3/7 = 1.

MATHEMATICA

s={}; Do[r = 1 - n/DivisorSigma[1, n]; Do[If[m/DivisorSigma[1, m] == r, AppendTo[s, m]], {m, 1, n-1}], {n, 1, 1000}]; s (* Amiram Eldar, Jun 24 2019 *)

PROG

(PARI) nbsh(n) = {v = []; vn = n/sigma(n); for (m=1, n-1, if (m/sigma(m) + vn == 1, v = concat(v, m)); ); return (v); }

lista(nn) = {for (n=1, nn, for (i=1, #nbshn, print1(nbshn[i], ", ")); ); }

CROSSREFS

Cf. A000203, A002025, A002046, A017665, A017666, A253534.

Sequence in context: A016072 A335163 A095867 * A349171 A338658 A344224

Adjacent sequences:  A253532 A253533 A253534 * A253536 A253537 A253538

KEYWORD

nonn

AUTHOR

Michel Marcus, Jan 03 2015

STATUS

approved

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Last modified August 17 08:02 EDT 2022. Contains 356184 sequences. (Running on oeis4.)