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Talk:Zumkeller numbers: Difference between revisions
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1344 4 994593600</pre>
[[user Horsth|Horsth]] 06:28, 20 June 2021 (UTC)
== Cheating odd no 5 zumkeller numbers ==
there are more restrictions for finding those zumkeller numbers quick:
The first not divisible by 3^2*7 aka 63 is #204:6,789,783
<pre>
203:6729723 : 80 : 3^4*7*11*13*83_chk_6729723<_SoD_13660416<
6830208 = 21+117+1079+11869+87399+6729723 = 6830208
204:6789783 : 96 : 3*7^2*11*13*17*19_chk_6789783<_SoD_13789440<
6894720 = 931+15827+88179+6789783 = 6894720
205:6837831 : 96 : 3^3*7*11^2*13*23_chk_6837831<_SoD_14300160<
7150080 = 3+33+759+14157+297297+6837831 = 7150080</pre>
The first not divisible by 3*7 aka 21 is #908:28,683,369
<pre>
907:28639611 :108 : 3^2*7*11^2*13*17^2_chk_28639611<_SoD_59449936<
29724968 = 9+187+17017+200277+867867+28639611 = 29724968
908:28683369 :128 : 3^3*11*13*17*19*23_chk_28683369<_SoD_58060800<
29030400 = 19+57+1311+55913+289731+28683369 = 29030400
909:28765737 : 96 : 3^2*7*11*13*31*103_chk_28765737<_SoD_58146816<
29073408 = 1+9+63+143+2163+14729+290563+28765737 = 29073408</pre>
It might be possible that those numbers aren't divisible by 3.
Replace 5 by 7. Therefor it must be a very large number.
<pre>
first zumkeller not divible by 2 or 3
0: 5,391,411,025 :384 : 5^2*7*11*13*17*19*23*29_SoD_10799308800
this:46,797,447,697 :768 : 7^2*11*13*17*19*23*29*31 is to small
</pre>
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