The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002545 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A002545

Numerator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).
(history; published version)

#42 by Alois P. Heinz at Sat Nov 17 20:45:11 EST 2018

STATUS

editing

approved

#41 by Alois P. Heinz at Sat Nov 17 20:44:49 EST 2018

DATA

1, 3, 7, 15, 29, 469, 29531, 1303, 16103, 190553, 128977, 9061, 30946717, 39646461, 58433327, 344499373, 784809203, 169704792667, 665690574539, 5667696059, 337284946763, 7964656853269, 46951444927823, 284451446729, 1597747168263479, 816088653136373

#40 by Alois P. Heinz at Sat Nov 17 20:43:44 EST 2018

MAPLE

with(combinat):seq(numer(stirling1-Stirling1(j+3, , 3)/(j+3)!*3!*(-1)^j), j=03..50); # Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

STATUS

proposed

editing

#39 by Jon E. Schoenfield at Sat Nov 17 20:23:31 EST 2018

STATUS

editing

proposed

#38 by Jon E. Schoenfield at Sat Nov 17 20:22:13 EST 2018

NAME

Numerator of sum 1/(Sum_{i*+j*+k) for =n; i,j,k > 0 and } 1/(i+*j+*k=n).

COMMENTS

For prime p >= 5, a(p) == -2*Bernoulli(p-3) (mod p). (see See Zhao link). ) - Michel Marcus, Feb 05 2016

MATHEMATICA

Table[Sum[1/i/j/(n-i-j), {i, n-2}, {j, n-i-1}], {n, 3, 100}] (* _Ryan Propper _ *)

STATUS

approved

editing

Discussion

Sat Nov 17

20:23

Jon E. Schoenfield: Reformatting of Name okay?

#37 by Max Alekseyev at Wed Feb 17 14:55:32 EST 2016

STATUS

editing

approved

#36 by Max Alekseyev at Wed Feb 17 14:54:10 EST 2016

COMMENTS

For prime p>=5, a(p) == -2*Bernoulli(p-3) (mod p). (see Zhao link). - Michel Marcus, Feb 05 2016

FORMULA

For prime p>=5, a(p) = -2*Bernoulli(p-3) mod p. (see Zhao link). - Michel Marcus, Feb 05 2016

STATUS

approved

editing

Discussion

Wed Feb 17

14:55

Max Alekseyev: My mistake, turning back into a congruence and moving it to Comments as it is not a formula (this a particular source of confusion).

#35 by Max Alekseyev at Wed Feb 17 09:56:03 EST 2016

STATUS

editing

approved

#34 by Max Alekseyev at Wed Feb 17 09:55:16 EST 2016

FORMULA

For prime p>=5, a(p) == -2*Bernoulli(p-3) mod p for p prime >= 5 . (see Zhao link). - Michel Marcus, Feb 05 2016

STATUS

approved

editing

Discussion

Wed Feb 17

09:55

Max Alekseyev: It's not a congrunce here. It's a binary mod operation. Hence, it should be equality "=",  not "==".

#33 by N. J. A. Sloane at Fri Feb 05 03:01:30 EST 2016

STATUS

editing

approved