A242627 -id:A242627 - cp's OEIS frontend

A165412 Divisors of 2520.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520

Offset: 1

Reinhard Zumkeller, Sep 17 2009

2520 is the largest and last of most highly composite numbers = A072938(7) = A002182(18) = 2520;
a(A000005(2520)) = a(48) = 2520 is the last term.
A242627(2520*n) = 9. - Reinhard Zumkeller, Jul 16 2014

Eric Weisstein's World of Mathematics, Highly Composite Number
Index entries for sequences related to divisors of numbers

Cf. A018336, A018357, A018388, A018412, A018444, A018490, A018559, and A018676 are subsets.

Cf. A018253, A018256, A018261, A018266, A018293, A018321, A018350, A018609, A178877, A178878, A178858, A178859, A178860, A178861, A178862, A178863, A178864.

Divisors[2520] (* Wesley Ivan Hurt, Mar 20 2022 *)

divisors(2520) \\ Charles R Greathouse IV, Jun 21 2017

A335037 a(n) is the number of divisors of n that are themselves divisible by the product of their digits.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 3, 3, 2, 6, 1, 3, 4, 4, 1, 5, 1, 4, 3, 3, 1, 8, 2, 2, 3, 4, 1, 6, 1, 4, 3, 2, 3, 8, 1, 2, 2, 5, 1, 5, 1, 4, 5, 2, 1, 8, 2, 3, 2, 3, 1, 5, 3, 5, 2, 2, 1, 8, 1, 2, 4, 4, 2, 5, 1, 3, 2, 4, 1, 10, 1, 2, 4, 3, 3, 4, 1, 5, 3, 2, 1, 7, 2, 2, 2, 5

Offset: 1

Bernard Schott, Jun 03 2020

Inspired by A332268.
A number that is divisible by the product of its digits is called Zuckerman number (A007602); e.g., 24 is a Zuckerman number because it is divisible by 2*4=8 (see links).
a(n) = 1 iff n = 1 or n is prime not repunit >= 13.
a(n) = 2 iff n is prime = 2, 3, 5, 7 or a prime repunit.
Numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 111111111111111111111 (repunit with 19 times 1's) have all divisors Zuckerman numbers. The sequence of numbers with all Zuckerman divisors is infinite iff there are infinitely many repunit primes (see A004023).

			For n = 4, the divisors are 1, 2, 4 and they are all Zuckerman numbers, so a(4) = 3.
For n = 14, the divisors are 1, 2, 7 and 14. Only 1, 2 and 7 are Zuckerman numbers, so a(14) = 3.

David A. Corneth, Table of n, a(n) for n = 1..10000
Giovanni Resta, Zuckerman numbers, Numbers Aplenty.
Gérard Villemin, Nombres de Zuckerman, Types de nombres.

Cf. A000005, A004023, A007602, A335038.

Similar with: A001227 (odd divisors), A087990 (palindromic divisors), A087991 (non-palindromic divisors), A242627 (divisors < 10), A332268 (Niven divisors).

zuckQ[n_] := (prodig = Times @@ IntegerDigits[n]) > 0&& Divisible[n, prodig]; a[n_] := Count[Divisors[n], ?(zuckQ[#] &)]; Array[a, 100] (* _Amiram Eldar, Jun 03 2020 *)

iszu(n) = my(p=vecprod(digits(n))); p && !(n % p);
a(n) = sumdiv(n, d, iszu(d)); \\ Michel Marcus, Jun 03 2020

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{n>=1} 1/A007602(n) = 3.26046... . - Amiram Eldar, Jan 01 2024

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A165412 Divisors of 2520.

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