A356659 - OEIS

%I #15 Oct 09 2022 09:42:18

%S 9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,35,36,39,40,42,

%T 44,45,48,50,51,52,54,55,56,57,60,63,64,65,66,68,70,72,75,76,77,78,80,

%U 81,84,85,88,90,92,96,98,99,100,102,104,105,108,110,112,114,117,120,125

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

%C If k is in the sequence then so is k*m. - _David A. Corneth_, Oct 08 2022

%H David A. Corneth, <a href="/A356659/b356659.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n + t) = a(n) + s for some finite t and s. - _David A. Corneth_, Oct 08 2022

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

%o (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); }

%o 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

%Y 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).

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Aug 20 2022