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Numbers representable as x^y * y + y, where x>1 and y>1 are integers.
1

%I #12 Jan 16 2015 10:21:32

%S 10,20,27,34,52,68,74,84,100,130,164,165,195,202,244,290,328,340,378,

%T 390,394,452,514,580,650,651,724,802,884,903,970,1028,1032,1060,1154,

%U 1220,1252,1354,1460,1539,1570,1684,1802,1924,2050,2056

%N Numbers representable as x^y * y + y, where x>1 and y>1 are integers.

%C The sequence of numbers z such that both z and z+1 are in the sequence begins:

%C 164, 650, 5187, 41474, 472394, 2654210, 10125002, 21233667, 30233090, 76236554, 169869314, 344373770, 648000002

%e a(1) = 10 = 2^2 * 2 + 2.

%e a(2) = 20 = 3^2 * 2 + 2.

%e a(3) = 27 = 2^3 * 3 + 3.

%e a(9) = 100 = 7^2 * 2 + 2.

%e a(11) = 164 = 9^2 * 2 + 2.

%e a(12) = 165 = 2^5 * 5 + 5.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Jan 11 2015