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A356659
Numbers k that can be written as the sum of 9 divisors of k (not necessarily distinct).
9
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 20 2022
STATUS
approved