|
Search: id:A090943
|
|
|
| A090943 |
|
Even numbers n such that N(n) is divisible by a nontrivial square, m^2, say, and GCD(n,m)=1, where N(n) is the numerator of the Bernoulli number B(n). The numbers m are given in A094095. |
|
+0
4
|
|
| 228, 284, 914, 1434, 1616, 2948, 3292, 4280, 4336, 5612, 5768, 6302, 6944, 7714, 7758, 8276, 9608
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
This sequence consists of the union of an infinite number of arithmetic progressions. Let p be an irregular prime and let {m1,m2,...} be even numbers < p(p-1) such that p^2 | N(mi). Then each (p,mi) is a second-order irregular pair. This leads to the arithmetic progression n=mi+p(p-1)k for each i and for k=0,1,2,3... If we restrict the sequence to those pairs with mi < 10000, we find that only the pairs (37,284), (59,914), (67,3292), (101,5768), (103,228), (157,6302) and (271,1434) contribute terms to this sequence.
|
|
LINKS
|
Bernd Kellner, Ueber irregulaere Paare hoeherer Ordnungen [On irregular pairs of higher order], Diplomarbeit, Goettingen 2002.
S. S. Wagstaff, Jr., Prime divisors of the Bernoulli and Euler numbers
|
|
MATHEMATICA
|
nn=10; s = Union[284 + 36*37*Range[0, nn], 914+58*59*Range[0, nn], 3292+66*67*Range[0, nn], 5768+100*101*Range[0, nn], 228+102*103*Range[0, nn], 6302+156*157*Range[0, nn], 1434+270*271*Range[0, nn]]; Select[s, #<=10000&]
|
|
CROSSREFS
|
Cf. A092681.
Sequence in context: A092324 A122976 A098245 this_sequence A128808 A043411 A053174
Adjacent sequences: A090940 A090941 A090942 this_sequence A090944 A090945 A090946
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Feb 27 2004
|
|
|
Search completed in 0.002 seconds
|
