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A120337
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Euler-irregular primes p dividing E(2k) for some 2k<p-1.
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1
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19, 31, 43, 47, 61, 67, 71, 79, 101, 137, 139, 149, 193, 223, 241, 251, 263, 277, 307, 311, 349, 353, 359, 373, 379, 419, 433, 461, 463, 491, 509, 541, 563, 571, 577, 587, 619, 677, 691, 709, 739, 751, 761, 769, 773, 811, 821, 877, 887, 907, 929, 941, 967, 971, 983
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| Wagstaff, Samuel S. Prime divisors of the Bernoulli and Euler numbers p. 357-374, 2002. MR 1956285
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LINKS
| Prime Pages, Euler Irregular
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FORMULA
| The (trivial) divisors of E(2n) are given by the theorem of Sylvester (1861): Let p prime with p=1 (mod 4), p-1|2n, p^k|2n then p^{k+1} | E(2n).
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EXAMPLE
| a(1) = 19 because 19 divides E(10) = -19*2659 and 10 + 1 < 19.
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MAPLE
| A120337_list := proc(bound)
local ae, F, p, m, maxp; F := NULL;
for m from 2 by 2 to bound do
p := nextprime(m+1);
ae := abs(euler(m));
maxp := min(ae, bound);
while p <= maxp do
if ae mod p = 0
then F := F, p fi;
p := nextprime(p);
od;
od;
sort([F]) end: # - Peter Luschny, Apr 25 2011
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CROSSREFS
| Cf. A092218, A120115.
Sequence in context: A178251 A164320 A154418 * A120115 A157995 A043298
Adjacent sequences: A120334 A120335 A120336 * A120338 A120339 A120340
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KEYWORD
| nonn
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AUTHOR
| Stefan Kraemer (skraemer(AT)math.uni-goettingen.de), Jun 22 2006
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EXTENSIONS
| Terms 251 through 983 from Peter Luschny, Apr 25 2011.
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