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Revision History for A106610

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A106610

Numerator of n/(n+9).
(history; published version)

#63 by Michael De Vlieger at Fri Nov 25 13:17:58 EST 2022

STATUS

reviewed

approved

#62 by Michel Marcus at Fri Nov 25 12:51:20 EST 2022

STATUS

proposed

reviewed

#61 by Michel Marcus at Fri Nov 25 12:51:17 EST 2022

STATUS

editing

proposed

#60 by Michel Marcus at Fri Nov 25 12:51:13 EST 2022

COMMENTS

In addition to being multiplicative, a(n) is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for n >= 1, m >= 1. In particular, a(n) is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, Feb 21 2019

STATUS

proposed

editing

#59 by Amiram Eldar at Fri Nov 25 01:56:33 EST 2022

STATUS

editing

proposed

#58 by Amiram Eldar at Fri Nov 25 01:10:35 EST 2022

KEYWORD

nonn,easy,frac,mult,changed

#57 by Amiram Eldar at Fri Nov 25 01:02:38 EST 2022

CROSSREFS

Cf. A008292, A109050.

Cf. A109050. Cf. Sequences given by the formula numerator(n/(n + k)): A026741 (k = 2), A051176 (k = 3), A060819 (k = 4), A060791 (k = 5), A060789 (k = 6), A106608 thru A106612 (k = 7 thru 11), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20).

#56 by Amiram Eldar at Fri Nov 25 01:02:06 EST 2022

COMMENTS

Apart from 0, also numerator of sumSum_{i=1..n} (1/((i+2)*(i+3)), i=1..n) = n/(3n+9). - Bruno Berselli, Nov 07 2012

REFERENCES

Raffaello Giusti, editore, Supplemento al Periodico di Matematica (Livorno), Jul 1902. , p. 138 (Problem 421, case k=3).

#55 by Amiram Eldar at Fri Nov 25 01:01:10 EST 2022

REFERENCES

"Raffaello Giusti, editore, Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), Jul 1902 . p. 138 (Problem 421, case k=3).

LINKS

P. Peter Bala, <a href="/A306367/a306367.pdf">A note on the sequence of numerators of a rational function </a>, 2019.

#54 by Amiram Eldar at Fri Nov 25 00:59:15 EST 2022

COMMENTS

Multiplicative with a(3^e) = 3^max(0,e-2), a(p^e) = p^e if p<>3. - R. J. Mathar, Apr 18 2011

FORMULA

Dirichlet g.f. zeta(s-1)*(1-2/3^s-2/9^s). (End)

Multiplicative with a(3^e) = 3^max(0,e-2), a(p^e) = p^e if p<>3. (End)