A356659 Numbers k that can be written as the sum of 9 divisors of k (not necessarily distinct).

9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 50, 51, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 70, 72, 75, 76, 77, 78, 80, 81, 84, 85, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 125

Offset: 1

Author

Wesley Ivan Hurt, Aug 20 2022

Keywords

• nonn

Comments

If k is in the sequence then so is k*m. - David A. Corneth, Oct 08 2022

Examples

			14 is in the sequence since 14 = 2+2+2+2+2+1+1+1+1, where each summand divides 14.
		

Links

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

Crossrefs

Numbers k that can be written as the sum of j divisors of k (not necessarily distinct) for j=1..10: A000027 (j=1), A299174 (j=2), A355200 (j=3), A354591 (j=4), A355641 (j=5), A356609 (j=6), A356635 (j=7), A356657 (j=8), this sequence (j=9), A356660 (j=10).

Programs

PARI

upto(n) = { my(v = vector(n,i,-1), t = 0); for(i = 1, n, if(v[i] == -1, print1(i", "); v[i] = is(i, 9); if(v[i] == 1, for(j = 2, n \ i, v[i*j] = 1; ) ) ); ); select(x->x >= 1, v, 1); }
is(n, {qd = 10}) = { my(d = divisors(n)); d = d[^#d]; forvec(x = vector(qd-1, i, [1, #d]), s = sum(i = 1, qd-1, d[x[i]]); if(n - s >= d[x[qd - 1]], if(n % (n - s) == 0, return(1); ) ) , 1 ); 0 } \\ David A. Corneth, Oct 08 2022

Formula

a(n + t) = a(n) + s for some finite t and s. - David A. Corneth, Oct 08 2022