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

8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 76, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 136, 138, 140, 144, 150, 152, 154, 156, 160, 162, 168, 170, 174, 176

Offset: 1

Author

Wesley Ivan Hurt, Aug 20 2022

Keywords

• nonn

Comments

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

Examples

			14 is in the sequence since 14 = 2+2+2+2+2+2+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), this sequence (j=8), A356659 (j=9), A356660 (j=10).

Programs

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

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