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A327714 Exceptional class of numbers n such that p(7*n + 5) == 0 mod 49, where p() = A000041(). 7
73, 98, 99, 112, 141, 154, 171, 197, 225, 245, 266, 276, 283, 288, 290, 301, 309, 316, 322, 323, 330, 357, 385, 386, 406, 414, 444, 455, 463, 465, 483, 484, 491, 498, 512, 525, 539, 554, 575, 596, 602, 626, 654, 665, 679 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The unexceptional class consists of the numbers n == (2, 4, 5, or 6) mod 7. Watson (1938, p. 125) proved that such numbers n satisfy p(7*n + 5) == 0 mod 49.

LINKS

Table of n, a(n) for n=1..45.

Watson, G. N., Ramanujans Vermutung √ľber Zerf√§llungsanzahlen, J. Reine Angew. Math. (Crelle) 179 (1938), 97-128; see pp. 124-127.

EXAMPLE

p(7*73 + 5) = p(516) = 49 * 113094142490063549717. This example is given by Watson (1938, p. 127). On the same page, he also says that p(105*7 + 5) = p(740) == 0 mod 49 (even though 105 == 0 mod 7), but that is wrong.

MAPLE

isA327714 := n -> 0 = modp(combinat:-numbpart(7*n + 5), 49) and 2 <> modp(n, 7) and 4 <> modp(n, 7) and 5 <> n mod 7 and 6 <> n mod 7;

select(isA327714, [$ (1 .. 700)]);

CROSSREFS

Cf.  A000041, A110375, A160524, A327713.

Sequence in context: A146354 A050958 A139990 * A179154 A116210 A180522

Adjacent sequences:  A327711 A327712 A327713 * A327715 A327716 A327717

KEYWORD

nonn

AUTHOR

Petros Hadjicostas, Sep 23 2019

STATUS

approved

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Last modified August 14 08:08 EDT 2020. Contains 336480 sequences. (Running on oeis4.)