A290574 Self numbers that are the product of two self numbers greater than one.

9, 378, 400, 525, 602, 1155, 1188, 1862, 2055, 2200, 2325, 2415, 2492, 2560, 2907, 3045, 3348, 3392, 3460, 3515, 3717, 3752, 3965, 4180, 4360, 4382, 4415, 4865, 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

Offset: 1

Author

Peter Weiss, Aug 06 2017

Keywords

• nonn
• base

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003052, A290426.

Programs

Mathematica

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 *)
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 *)

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

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

Extensions

Corrected by Charles R Greathouse IV, Aug 23 2017