A323414 Numbers whose carryless sum of divisors is zero.

87, 95, 540, 608, 973, 5940, 7906, 8787, 9595, 9715, 54540, 63796, 64648, 83337, 599940, 796677, 836169, 972223, 5459940, 6406408, 6441128, 6464648, 7165526, 8091755, 9514464, 54049140, 54599940, 64006408, 64064648, 64640648, 82913331

Offset

1,1

Comments

Equivalently, numbers k such that A323394(k) = 0.

Links

Table of n, a(n) for n=1..31.

Index entries for sequences related to carryless arithmetic

Example

For k = 87:
- the divisors of 87 are: 1, 3, 29, 87,
- the sum of units is: 1 + 3 + 9 + 7 = 20 == 0 (mod 10),
- the sum of tens is: 2 + 8 = 10 == 0 (mod 10),
- hence A323394(87) = 0 and 87 belongs to the sequence.

Prog

(PARI) isok(n, base=10) = my (v=[]); fordiv (n, d, my (w=Vecrev(digits(d, base))); v=vector(max(#v, #w), k, (if (k>#v, w[k], k>#w, v[k], (v[k]+w[k])%base)))); vecmax(v)==0

Crossrefs

Cf. A323394.

Sequence in context: A295698 A095597 A095583 * A231403 A256083 A038005

Adjacent sequences: A323411 A323412 A323413 * A323415 A323416 A323417

Keyword

nonn,base

Author

Rémy Sigrist, Jan 13 2019

Status

approved