OFFSET
1,2
COMMENTS
Called "perfect years". 1998 and 2114 are the nearest past and future examples.
REFERENCES
H. Herles, Reformstau, Gefuehlsstau, Verkehrsstau. Generalanzeiger, 12/31/1997, p. V.
H. Muller-Merbach and L. Logelix, Perfekte Jahre, Technologie und Management, Vol. 42, 1993, No. 1, p. 47 and No. 2, p. 95.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
H. Muller-Merbach, Wunsche für das "perfekte Jahr" 1998
EXAMPLE
1998 is perfect since 1*9*9*8/(1+9+9+8) = 24.
MAPLE
for n from 1 to 3000 do a := convert(n, base, 10):s := add(a[i], i=1..nops(a)):p := mul(a[i], i=1..nops(a)): if p<>0 and p mod s=0 then printf(`%d, `, n):fi:od:
MATHEMATICA
Select[Range[415], FreeQ[x = IntegerDigits[#], 0] && Divisible[Times @@ x, Plus @@ x] &] (* Jayanta Basu, Jul 13 2013 *)
PROG
(PARI) is(n) = my(d = digits(n)); vd = vecprod(d); vd != 0 && vd % vecsum(d) == 0 \\ David A. Corneth, Mar 15 2021
(Python)
from math import prod
def ok(n):
d = list(map(int, str(n)))
pod, sod = prod(d), sum(d)
return pod and pod%sod == 0
print([k for k in range(416) if ok(k)]) # Michael S. Branicky, Mar 28 2022
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Heiner Muller-Merbach (hmm(AT)sozwi.uni-kl.de), Jun 06 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org) and Vladeta Jovovic, Jun 07 2001
STATUS
approved