A098034 Numbers that are divisible both by the sum and by the product of the squares of their digits.

111, 11112, 1122112, 111111111, 122121216, 1111112112, 1111211136, 1116122112, 1211162112, 11111113116, 11111121216, 11112122112, 11121114112, 11132111232, 11133122112, 11213111232, 11311322112, 12111213312, 21111311232, 31111221312

Offset: 1

Author

Lekraj Beedassy, Sep 10 2004

Keywords

• nonn
• base

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

Examples

			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.
		

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)

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