

A131192


Numbers n >= 0 such that d(n) = (n^1 + 1)*(n^2 + 2)*...*(n^26 + 26) / 26! is nonintegral.


1



7, 11, 18, 24, 29, 37, 40, 50, 51, 62, 73, 76, 84, 89, 95, 102, 106, 115, 128, 139, 141, 150, 154, 161, 167, 172, 180, 183, 193, 194, 205, 206, 216, 219, 227, 245, 249, 258, 260, 271, 282, 284, 293, 297, 304, 310, 315, 323, 326, 336, 337, 348, 349, 362, 370, 375, 381, 388, 392, 403, 414, 425, 427, 436
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OFFSET

1,1


COMMENTS

Notice that 26! = 2^23 * 3^10 * 5^6 * 7^3 * 11^2 * 13^2 * 17 * 19 * 23. There is no divisibility for 11^2 and n in {11m+7} \ {121m+117} and for 13^2 and n in {13m+11} \ {169m+63}. Therefore, this sequence is formed by the union ( {11m+7} \ {121m+117} ) U ( {13m+11} \ {169m+63}).  Max Alekseyev, Nov 10 2007


LINKS

Table of n, a(n) for n=1..64.


MAPLE

d:=proc(n) options operator, arrow: (product(n^j+j, j=1..26))/factorial(26) end proc: a:=proc(n) if type(d(n), integer) = false then n else end if end proc; seq(a(n), n=1..300); # Emeric Deutsch, Oct 24 2007


CROSSREFS

Cf. A129995, A131189, A131190, A131191, A131685.
Sequence in context: A188074 A190689 A048215 * A195759 A130570 A106081
Adjacent sequences: A131189 A131190 A131191 * A131193 A131194 A131195


KEYWORD

nonn


AUTHOR

Alexander R. Povolotsky, Sep 25 2007


EXTENSIONS

Initial terms were calculated by Peter J. C. Moses; see comment in A129995
More terms from Emeric Deutsch, Oct 24 2007
More terms from Max Alekseyev, Feb 02 2015


STATUS

approved



