cp's OEIS Frontend

A356657 Numbers k that can be written as the sum of 8 divisors of k (not necessarily distinct).

%I A356657 #21 Sep 04 2022 12:28:00
%S A356657 8,10,12,14,16,18,20,22,24,26,28,30,32,36,40,42,44,48,50,52,54,56,60,
%T A356657 64,66,68,70,72,76,78,80,84,88,90,96,98,100,102,104,108,110,112,114,
%U A356657 120,126,128,130,132,136,138,140,144,150,152,154,156,160,162,168,170,174,176
%N A356657 Numbers k that can be written as the sum of 8 divisors of k (not necessarily distinct).
%C A356657 Terms are even. Proof by contradiction. Suppose m = a(n) is odd. Then each divisor is odd. Adding 8 odd numbers gives an even number. A contradiction. - _David A. Corneth_, Sep 02 2022
%H A356657 David A. Corneth, <a href="/A356657/b356657.txt">Table of n, a(n) for n = 1..10000</a>
%e A356657 14 is in the sequence since 14 = 2+2+2+2+2+2+1+1, where each summand divides 14.
%o A356657 (PARI) isok(k) = my(d=divisors(k)); forpart(p=k, if (setintersect(d, Set(p)) == Set(p), return(1)), , [8,8]); \\ _Michel Marcus_, Aug 21 2022
%o A356657 (PARI) is(n) = if(n % 2 == 1, return(0)); my(d = divisors(n)); forvec(x = vector(8, i, [1, #d-1]), s=sum(i=1, #x, d [x[i]]); if(n == s, print(vector(#x, j, d[x[j]]));return(1)), 1); 0 \\ _David A. Corneth_, Aug 21 2022
%Y A356657 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), this sequence (j=8), A356659 (j=9), A356660 (j=10).
%K A356657 nonn
%O A356657 1,1
%A A356657 _Wesley Ivan Hurt_, Aug 20 2022