The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A085080 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A085080

Smallest k such that n, k and n+k have the same prime signature (canonical form), or 0 if no such number exists.
(history; published version)

#73 by Alois P. Heinz at Fri Jan 27 21:49:17 EST 2023

STATUS

proposed

approved

#72 by Jon E. Schoenfield at Fri Jan 27 21:42:40 EST 2023

STATUS

editing

proposed

#71 by Jon E. Schoenfield at Fri Jan 27 21:42:32 EST 2023

EXAMPLE

a(36) = 0, because if a(n) exists then k exists such that k^2 + 36 = m^2 where k^2, 36 and m^2 have the same prime signature. Rewriting 36 = m^2 - k^2 = (m - k)*(m + k) and then inspection over divisors of 36 gives no terms. Alternatively checking Pythagorean triplets triples gives the same result. - David A. Corneth, Mar 08 2019

STATUS

approved

editing

#70 by Wesley Ivan Hurt at Wed Apr 10 03:49:25 EDT 2019

STATUS

proposed

approved

#69 by Michel Marcus at Wed Apr 10 03:39:33 EDT 2019

STATUS

editing

proposed

#68 by Michel Marcus at Wed Apr 10 03:39:29 EDT 2019

EXAMPLE

a(36) = 0, because if a(n) exist exists then k exist exists such that k^2 + 36 = m^2 where k^2, 36 and m^2 have the same prime signature. Rewriting 36 = m^2 - k^2 = (m - k)*(m + k) and then inspection over divisors of 36 gives no terms. Alternatively checking Pythagorean triplets gives the same result. - David A. Corneth, Mar 08 2019

STATUS

approved

editing

#67 by Bruno Berselli at Tue Apr 09 11:50:50 EDT 2019

STATUS

proposed

approved

#66 by David A. Corneth at Tue Apr 09 11:45:41 EDT 2019

STATUS

editing

proposed

#65 by David A. Corneth at Tue Apr 09 11:45:37 EDT 2019

COMMENTS

If n is even and a(n) > 0 and the exponent of 2 in the factorization of n is the largest in the prime signature then a(n) must be isn't necessarily odd. _Ray Chandler_ found n = 392 as an example where a(n) = 108 is even. (End)

STATUS

approved

editing

#64 by N. J. A. Sloane at Tue Mar 26 15:52:59 EDT 2019

STATUS

proposed

approved