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A167372 A120301(A123944(n))/A058313(A123944(n)) 0
5, 7, 11, 5, 13, 7, 17, 7, 37, 19, 29, 119, 47, 41, 23, 5, 29, 31, 37, 11, 37, 41, 43, 13, 7, 13, 71, 13, 49, 13, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A123944(n) = {19, 28, 87, 99, 104, 196, 203, 210, 222, 228, 231, 238, 281, 328, 367, 499, 579, 620, 888, 967, 1036, 1147, 1204, 1352, 1372, 1403, 1419, 1430, 1470, ...} Numbers n such that A120301(n) differs from A058313(n).

A120301(n) = {1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 52279, 95549, 1768477, 1632341, 167324635, 155685007, ...} Absolute value of numerator of the sum of all matrix elements of n X n matrix M[i,j] = (-1)^(i+j) * i/j, (i,j=1..n).

A058313(n) = {1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 52279, 95549, 1768477, 1632341, 33464927, 155685007, ...} Numerator of the n-th alternating harmonic number, sum ((-1)^(k+1)/k, k=1..n).

The ratio A120301(n)/A058313(n) = 1 for most n.

a(n) is prime for most n.

The first composite ratio a(12) = 119 = 7*17 corresponds to A123944(12) = 238.

Next two composite a(n) = 49 = 7^2 correspond to A123944 = 1470 and A123944 = 10290.

LINKS

Table of n, a(n) for n=1..31.

MATHEMATICA

f=0; Do[f=f+(-1)^(n+1)*1/n; g=Abs[(2(-1)^n*n+(-1)^n-1)/4]*f; rfg=Numerator[g]/Numerator[f]; If[(rfg==1)==False, Print[rfg]], {n, 1, 1500}]

CROSSREFS

Cf. A123944, A120301, A058313.

Sequence in context: A119653 A023592 A076546 * A023590 A096919 A023594

Adjacent sequences:  A167369 A167370 A167371 * A167373 A167374 A167375

KEYWORD

more,nonn

AUTHOR

Alexander Adamchuk, Nov 02 2009

STATUS

approved

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Last modified March 28 07:54 EDT 2017. Contains 284182 sequences.