A083367 Numbers k that are equal to the sum of its divisors after the digits of each divisor have been sorted in ascending order.

1, 60, 1959, 149587, 277947, 1449933, 2222863, 2396214, 24918486, 25354845, 48878262, 1673533845, 24753647943

Offset: 1

Author

Jason Earls, Jun 11 2003

Keywords

• nonn
• base
• more

Comments

No more terms through 10^8. - Ryan Propper, Sep 09 2005

a(13) > 10^10. - Donovan Johnson, Aug 28 2013

a(14) > 10^11. - Giovanni Resta, Aug 30 2013

Examples

			a(3) = 1959 because the divisors of 1959 are [1, 3, 653, 1959] and 1+3+356+1599 = 1959.
		

Crossrefs

Cf. A004185.

Programs

Mathematica

Do[l = IntegerDigits /@ Divisors[n]; l = Map[Sort[ # ]&, l]; k = Plus @@ Map[FromDigits[ # ]&, l]; If[k == n, Print[n]], {n, 1, 10^8}] (* Ryan Propper, Sep 09 2005 *)
Select[Range[24*10^5],Total[FromDigits[Sort[IntegerDigits[#]]]&/@Divisors[#]] == #&] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Dec 28 2022 *)

PARI

is(n) = sumdiv(n,d,fromdigits(vecsort(digits(d))))==n \\ David A. Corneth, Dec 28 2022

Python

from sympy import divisors
def sa(n): return int("".join(sorted(str(n))))
def ok(n): return n == sum(sa(d) for d in divisors(n, generator=True))
print([k for k in range(1, 3*10**5) if ok(k)]) # Michael S. Branicky, Dec 28 2022

Extensions

More terms from Ryan Propper, Sep 09 2005

a(12) from Donovan Johnson, Aug 28 2013

a(13) from Giovanni Resta, Aug 30 2013