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A346641 Numbers k with at least one partition into two parts (s,t), s<=t such that t | s*k but no proper divisor of k has this property.

%I A346641 #19 Jan 25 2022 13:56:58
%S A346641 2,15,35,63,77,91,99,117,143,153,187,209,221,247,299,323,325,357,391,
%T A346641 399,425,437,475,483,493,513,527,551,575,589,609,621,651,667,703,713,
%U A346641 725,759,775,777,783,837,851,861,899,925,943,957,989,999,1023,1025,1073,1075
%N A346641 Numbers k with at least one partition into two parts (s,t), s<=t such that t | s*k but no proper divisor of k has this property.
%C A346641 Primitive subsequence of A350803.
%C A346641 Odd terms form primitive subsequence of A090196. - _Bernard Schott_, Jan 23 2022
%H A346641 David A. Corneth, <a href="/A346641/b346641.txt">Table of n, a(n) for n = 1..10000</a>
%e A346641 k = 15 = 6 + 9 = s + t is in the sequence (t = 9 | 6*15 = 90 = s*k) but no proper divisor of 15 has this property.
%o A346641 (PARI) upto(n) = { my(v = vector(n, i, -1)); for(i = 1, n, if(v[i] == -1, if(isA350803(i), v[i] = 1; for(j = 2, n\i, v[i*j] = 0; ) ) ) ); select(x->x==1, v, 1) }
%o A346641 isA350803(n) = { for(i = 1, n\2, if((n*i)%(n-i) == 0, return(1) ) ); return(0) }
%Y A346641 Cf. A350803.
%Y A346641 Subsequence: A082663.
%K A346641 nonn
%O A346641 1,1
%A A346641 _David A. Corneth_, Jan 22 2022