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A098034 Numbers that are divisible both by the sum and by the product of the squares of their digits. 1
111, 11112, 1122112, 111111111, 122121216, 1111112112, 1111211136, 1116122112, 1211162112, 11111113116, 11111121216, 11112122112, 11121114112, 11132111232, 11133122112, 11213111232, 11311322112, 12111213312, 21111311232, 31111221312 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also called "uncommon numbers". Sequence contains the repunits R_m, where m=A014950,m>1. - Lekraj Beedassy, Jul 14 2008

Called "insolite numbers" in the paper by J.-M. De Koninck and N. Doyon, which contains a list of insolite numbers below 10^18. Their list lacks a(63)=112264112111616. They conjectured that 1111111111131111131111111111175 is the smallest insolite number containing the digit '5'. I verified this claim and found a further such number, 1111111111111111117111111111911111375, which may not be the second one. - Giovanni Resta, Oct 19 2012

REFERENCES

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 111, p. 39, Ellipses, Paris 2008.

LINKS

Lekraj Beedassy and Giovanni Resta, Table of n, a(n) for n = 1..428 (terms < 10^20, first 39 terms from Lekraj Beedassy)

J.-M. De Koninck and N. Doyon, On a very thin sequence of integers, Annales Rolando Eötvös Nominatae, 20:157-177 (2001)

EXAMPLE

1122112 is in the sequence because 1^2 + 1^2 + 2^2 + 2^2 + 1^2 + 1^2 + 2^2=16,(1*1*2*2*1*1*2)^2=64 and we have 1122112=16*70132=64*17533.

CROSSREFS

Sequence in context: A259102 A262629 A111864 * A109242 A165155 A078270

Adjacent sequences:  A098031 A098032 A098033 * A098035 A098036 A098037

KEYWORD

nonn,base

AUTHOR

Lekraj Beedassy, Sep 10 2004

EXTENSIONS

More terms from Lekraj Beedassy, Jul 14 2008

Missing term a(11) inserted, b-file corrected and extended to terms < 10^20 by Giovanni Resta, Oct 19 2012

STATUS

approved

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Last modified September 19 15:43 EDT 2020. Contains 337178 sequences. (Running on oeis4.)