cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A076090 a(1) = 1; for n > 1, smallest number > 1 which is the n-th power of the sum of its digits, or 0 if no such number exists.

Original entry on oeis.org

1, 81, 512, 2401, 17210368, 34012224, 612220032, 20047612231936, 3904305912313344, 13744803133596058624, 8007313507497959524352, 2518170116818978404827136, 81920000000000000
Offset: 1

Views

Author

Amarnath Murthy, Oct 07 2002

Keywords

Examples

			a(3) = 512 = 8^3 and no smaller number (>1) can have this property. (This has been established in the reference.)

References

  • Amarnath Murthy, The largest and the smallest m-th power whose digits sum /product is its m-th root. To appear in Smarandache Notions Journal.
  • Amarnath Murthy, e-book, " Ideas on Smarandache Notions " MS.LIT

Crossrefs

Cf. A046017.

Formula

For n > 1, a(n) = A046017(n)^n. - David Wasserman, Mar 25 2005
a(n)=A072408(n), n>1. [From R. J. Mathar, Sep 23 2008]

Extensions

More terms from David Wasserman, Mar 25 2005

A352742 a(n) is the smallest number > 1 that is not divisible by 10 but is divisible by the n-th power of the sum of its digits.

Original entry on oeis.org

2, 81, 512, 2401, 11101212, 34012224, 612220032, 20047612231936, 3904305912313344, 7800803212802061312, 1025300207121086650406, 213780015477322248820322, 14076019706120526112710656, 2670419511272061205254504361, 2759031540715333904109053133443, 10530400808911150200350000010411
Offset: 1

Views

Author

Nicolas Bělohoubek, Mar 31 2022

Keywords

Comments

a(n+1) >= a(n).
When A072408(n) is not multiple of 10 then a(n) <= A072408(n).
a(n) = m * k^n where m is a positive integer and k is the sum of digits of a(n).
Conjecture: No term is a multiple of 5.
a(28) = 265^28, disproving the above conjecture. - Charles R Greathouse IV, Apr 02 2022

Examples

			For n=5, 11101212 is not divisible by 10 but is divisible by the 5th power of the sum of its digits, that being (1+1+1+0+1+2+1+2)^5 = 9^5. There is no smaller such number.

Crossrefs

Cf. A072408.

Extensions

a(7)-a(8) confirmed by Jon E. Schoenfield, Mar 31 2022
a(9)-a(16) from Charles R Greathouse IV, Apr 02 2022
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.