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A355620
a(n) is the sum of the divisors of n whose decimal expansions appear as substrings in the decimal expansion of n.
3
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
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.
MATHEMATICA
Table[DivisorSum[n, # &, StringContainsQ[IntegerString[n], IntegerString[#]] &], {n, 100}] (* Paolo Xausa, Jul 23 2024 *)
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jul 10 2022
STATUS
approved