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

1,1

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

Links

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

Example

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

Prog

(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

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).

Sequence in context: A080752 A262159 A020744 * A008557 A378174 A161425

Adjacent sequences: A356654 A356655 A356656 * A356658 A356659 A356660

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 20 2022

Status

approved