A355620 a(n) is the sum of the divisors of n whose decimal expansions appear as substrings in the decimal expansion of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 14, 15, 21, 17, 18, 19, 20, 22, 22, 24, 23, 30, 30, 28, 27, 30, 29, 33, 32, 34, 36, 34, 40, 45, 37, 38, 42, 44, 42, 44, 43, 48, 50, 46, 47, 60, 49, 55, 52, 54, 53, 54, 60, 56, 57, 58, 59, 66, 62, 64, 66, 68, 70, 72, 67

Offset

1,2

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of the first 100000 terms (red pixels indicate when n is a multiple of 10)

Index entries for sequences related to decimal expansion of n

Index entries for sequences related to divisors

Formula

a(n) >= n.

a(n) <= A000203(n) with equality iff n belongs to A239058.

a(10^n) = A002275(n+1) for any n >= 0.

Example

For n = 110:
- the divisors of 110 are: 1, 2, 5, 10, 11, 22, 55, 110,
- 1, 10, 11 and 110 appear as substrings in 110,
- so a(110) = 1 + 10 + 11 + 110 = 132.

Prog

(PARI) a(n, base=10) = { my (d=digits(n, base), s=setbinop((i, j) -> fromdigits(d[i..j], base), [1..#d]), v=0); for (k=1, #s, if (s[k] && n%s[k]==0, v+=s[k])); return (v) }
(Python)
from sympy import divisors
def a(n):
    s = str(n)
    return sum(d for d in divisors(n, generator=True) if str(d) in s)
print([a(n) for n in range(1, 68)]) # Michael S. Branicky, Jul 10 2022

Crossrefs

Cf. A000203, A002275, A121041, A121042, A239058, A355633 (binary analog).

Sequence in context: A182175 A254329 A128870 * A256476 A154771 A071249

Adjacent sequences: A355617 A355618 A355619 * A355621 A355622 A355623

Keyword

nonn,base

Author

Rémy Sigrist, Jul 10 2022

Status

approved