A365762 Greatest common divisor of n and the product of its digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 20, 1, 2, 1, 8, 5, 2, 1, 4, 1, 30, 1, 2, 3, 2, 5, 18, 1, 2, 3, 40, 1, 2, 1, 4, 5, 2, 1, 16, 1, 50, 1, 2, 1, 2, 5, 2, 1, 2, 1, 60, 1, 2, 9, 8, 5, 6, 1, 4, 3, 70, 1, 2, 1, 2, 5, 2, 7, 2, 1, 80, 1, 2, 1, 4, 5, 2, 1, 8, 1, 90, 1, 2, 3, 2, 5, 6, 1, 2, 9, 100

Offset

1,2

Comments

This sequence will contain all numbers whose prime factors are exclusively <10 (7-smooth numbers, A002473).

Links

Table of n, a(n) for n=1..100.

Example

a(11)=1 as 1*1=1; 11 and 1 share 1 as a gcd.
a(15)=5 as 1*5=5; 15 and 5 share 5 as a gcd.
a(10)=10 as 1*0=0; 10 and 0 share 10 as a gcd.

Mathematica

a[n_]:=GCD[n, Product[Part[IntegerDigits[n], i], {i, IntegerLength[n]}]]; Array[a, 100] (* Stefano Spezia, Sep 20 2023 *)

Prog

(Python)
from math import gcd, prod
def a(n): return gcd(n, prod(map(int, str(n))))
print([a(n) for n in range(1, 101)])
(PARI) a(n) = gcd(n, vecprod(digits(n))); \\ Michel Marcus, Sep 20 2023

Crossrefs

Cf. A066750, A007954, A002473, A214587.

Sequence in context: A322629 A190599 A214587 * A010889 A053831 A263131

Adjacent sequences: A365759 A365760 A365761 * A365763 A365764 A365765

Keyword

nonn,base,easy

Author

Simon R Blow, Sep 18 2023

Status

approved