[seqfan] super-divisor

[юрий герасимов]

Dear SeqFans.....

Super-divisor m of k: numbers m such that k/m + k divides (k/m)^(k/m) + k, (k/m)^k + k/m and k^(k/m) + k/m (definition).

Number of super-divisors of n: 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1,...

Conjecture: a(n) = 0 or 1 for all n....................................................................................................................................

Super-divisor m of n, or 0 if no such m exists: 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 4, 1, 0, 1, 0, ...

Smallest k such that super-divisor of k is equal to n: 2, 1, 10, 0, 36, 0, 78, 0, 136, 0, 210, 0, 312, 0, 406, 0, ...

1 = odd super-divisor m of 2n + 1  or A005408: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, ...

m = even super-divisor of m*(2m + 2)*n + m*(2m + 1) for all n......................................... Examples:

2 = even super-divisor of 2*(2*2 + 2)*n + 2*(2*2 + 1) = 12n + 10  or A017641: 10, 22, 34, 46, 58, 70, 82, 94, ...

4 = even super-divisor of 4*(2*4 + 4)*n + 4*(2*4 + 1) = 40n + 36: 36, 76, 116, 156, 196, 236, 276, 316, 356, ...

6 = even super-divisor of 6*(2*6 + 6)*n + 6*(2*6 + 1) = 84n + 78: 78, 162, 246, 330, 414, 498, 582, 666, ...

8 = even super-divisor of 8*(2*8 + 8)*n + 8*(2*8 + 1) = 144n + 136: 136, 280, 424, 568, 712, 856, 1000, ...

10 = even super-divisor of 10*(2*10 + 10)*n + 10*(2*10 + 1) = 220n + 210: 210, 430, 650, 870, 1090, ...

Numbers n without super-divisors: 2, 4, 8, 12, 14, 16, 18, 20, 24, 26, 28, 30, 32, 38, 40, 42, 44, 48, 50,...

[Dec 15 2014] "I was intending to include this ...{sequences], but am getting a message saying I have "too many edits pending".
I only have three pending edits; I used to be allotted seven. So...
1) Can someone please include this...[sequences] for ...[OEIS}.   I'm not looking for an attribution, I just would like to see it posted.
2) Can anyone explain the new (low) editing limit?   Has there been a policy change?
Thanks,
Bob Selcoe" [and Juri-Stepan Gerasimov]..