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

1,1

Comments

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

Links

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

Formula

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

Example

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

Prog

(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

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).

Sequence in context: A119956 A059102 A295743 * A214602 A167819 A120185

Adjacent sequences: A356656 A356657 A356658 * A356660 A356661 A356662

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 20 2022

Status

approved