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Self numbers that are the product of two self numbers greater than one.
1

%I #18 Nov 09 2018 21:32:25

%S 9,378,400,525,602,1155,1188,1862,2055,2200,2325,2415,2492,2560,2907,

%T 3045,3348,3392,3460,3515,3717,3752,3965,4180,4360,4382,4415,4865,

%U 4920,5115,5418,5517,5719,6138,6228,6900,7038,7060,7396,7532,7565,7609,7947,8162,8342,8465,8520,8700,8757,8869,8970,9152,9365,9387,9409,9420,9422,9499,9870,9925

%N Self numbers that are the product of two self numbers greater than one.

%H Charles R Greathouse IV, <a href="/A290574/b290574.txt">Table of n, a(n) for n = 1..10000</a>

%e The product of the self numbers 31 and 75 is the self number 2325, so 2325 is in the sequence.

%t Block[{nn = 10^4, s}, s = Rest@ Complement[Range@ nn, Union[Table[n + Total@ IntegerDigits@ n, {n, nn}]]]; Select[Range@ nn, Function[n, And[MemberQ[s, n], AnyTrue[Map[{#, n/#} &, Rest@ TakeWhile[Divisors@ n, # <= Sqrt@ n &]], AllTrue[#, MemberQ[s, #] &] &]]]]] (* or *)

%t Block[{nn = 5000, s}, s = Rest@ Complement[Range@ nn, Union@ Table[n + Total@ IntegerDigits@ n, {n, nn}]]; Select[Union@ Sort@ Map[Times @@ # &@ # &, Tuples[s, {2}]], MemberQ[s, #] &]] (* _Michael De Vlieger_, Aug 23 2017, after _T. D. Noe_ at A003052 *)

%o (PARI) is(n)=if(!is_A003052(n), return(0)); fordiv(n,d, if(d==1, next); if(d^2>n, break); if(is_A003052(d) && is_A003052(n/d), return(1))); 0 \\ _Charles R Greathouse IV_, Aug 23 2017

%o (PARI) is_A290574(n)={is_A003052(n) && fordiv(n,d, d^2>n && break; d>1 && is_A003052(d) && is_A003052(n/d) && return(1))} \\ _M. F. Hasler_, Nov 09 2018

%Y Cf. A003052, A290426.

%K nonn,base

%O 1,1

%A _Peter Weiss_, Aug 06 2017

%E Corrected by _Charles R Greathouse IV_, Aug 23 2017