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%I #14 Feb 02 2015 21:47:18
%S 2,7,12,18,22,27,29,37,40,47,51,52,62,72,73,77,84,87,95,97,102,106,
%T 112,122,127,128,137,139,147,150,152,161,162,172,177,183,187,194,197,
%U 202,205,212,216,222,227,237,247,249,252,260,262,271,272,277,282,287,293,297,302,304,312,315,322,326,327,337
%N Numbers n>=0 such that d(n) = (n^1 + 1) (n^2 + 2) ... (n^25 + 25) / 25! is nonintegral.
%C If n is in this sequence the so is n+6050. - _Max Alekseyev_, Feb 02 2015
%F Notice that 25! = 2^22 * 3^10 * 5^6 * 7^3 * 11^2 * 13 * 17 * 19 * 23. The value of (n^1+1)(n^2+2)...(n^25+25) is always divisible by all these prime powers, except 5^6 and 11^2. There is no divisibility by 5^6 for n in {50m+2, 50m+12, 50m+22, 50m+27, 50m+37, 50m+47} and by 11^2 for n in {11m+7} \ {121m+117}. Therefore, the sequence is the union {50m+2} U {50m+12} U {50m+22} U {50m+27} U {50m+37} U {50m+47} U ( {11m+7} \ {121m+117} ). - _Max Alekseyev_, Nov 10 2007
%o (PARI) { is_A131190(n) = setsearch([2,12,22,27,37,47],n%50) || ( (n%11)==7 && (n%121)!=117 ) } /* _Max Alekseyev_, Feb 02 2015 */
%Y Cf. A129995, A131189, A131191, A131192, A131685
%K nonn
%O 1,1
%A _Alexander R. Povolotsky_, Sep 25 2007
%E Initial terms were calculated by _Peter J. C. Moses_; see comment in A129995.
%E More terms from _Max Alekseyev_, Feb 02 2015
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