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.

2, 15, 35, 63, 77, 91, 99, 117, 143, 153, 187, 209, 221, 247, 299, 323, 325, 357, 391, 399, 425, 437, 475, 483, 493, 513, 527, 551, 575, 589, 609, 621, 651, 667, 703, 713, 725, 759, 775, 777, 783, 837, 851, 861, 899, 925, 943, 957, 989, 999, 1023, 1025, 1073, 1075

Offset: 1

Author

David A. Corneth, Jan 22 2022

Keywords

• nonn

Comments

Primitive subsequence of A350803.

Odd terms form primitive subsequence of A090196. - Bernard Schott, Jan 23 2022

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A350803.

Subsequence: A082663.

Programs

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) }
isA350803(n) = { for(i = 1, n\2, if((n*i)%(n-i) == 0, return(1) ) ); return(0) }