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A061013 Numbers n such that (product of digits of n) is divisible by (sum of digits of n), where 0's are not permitted. 3
1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 36, 44, 63, 66, 88, 123, 132, 138, 145, 154, 159, 167, 176, 183, 189, 195, 198, 213, 224, 231, 235, 242, 246, 253, 257, 264, 268, 275, 279, 286, 297, 312, 318, 321, 325, 333, 345, 347, 352, 354, 357, 369, 374, 375, 381, 396, 415 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Called "perfect years". 1998 and 2114 are recent 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

Table of n, a(n) for n=1..57.

H. Muller-Merbach, Wunsche fuer 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 *)

CROSSREFS

See A038367 for case where 0 digits are allowed. Cf. A055931.

Sequence in context: A062998 A108194 A083158 * A037264 A045910 A128290

Adjacent sequences:  A061010 A061011 A061012 * A061014 A061015 A061016

KEYWORD

easy,nonn,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

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Last modified September 2 10:05 EDT 2014. Contains 246350 sequences.