OFFSET
1,1
COMMENTS
Zerosuperdivisor numbers. Numbers n such that A247477(n) = 0.
A000027 = zerosuperdivisor numbers U onesuperdivisor numbers U twosuperdivisor numbers U threesuperdivisor numbers U ...
Conjecture: Perfect numbers (A000396) are zerosuperdivisor numbers.
Conjecture: Average of twin prime pairs (A014574) are zerosuperdivisor numbers.
None of these numbers are odd or 10 mod 12 or 36 mod 40 or 78 mod 84 or 136 mod 144 or ... - Charles R Greathouse IV, Feb 19 2015
LINKS
Michael De Vlieger and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 3592 terms from Michael De Vlieger)
EXAMPLE
2 is in this sequence because 2/1 + 2 does not divide (2/1)^(2/1) + 2, (2/1)^2 + 2/1, 2^(2/1) + 2/1 and 2/2 + 2 does not divide (2/2)^(2/2) + 2, (2/2)^2 + 2/2, 2^(2/2) + 2/2: 4 does not divide 6, 6, 6 and 3 does not divide 3, 2, 3.
MATHEMATICA
superdivisors[n_] := Select[Range@ n, And[Mod[(n/#)^(n/#) + n, n/# + n] == 0, Mod[(n/#)^n + n/#, n/# + n] == 0, Mod[n^(n/#) + n/#, n/# + n] == 0] &] /. {} -> 0; Position[Array[superdivisors, 174], 0] // Flatten (* Michael De Vlieger, Feb 09 2015 *)
PROG
(PARI) is(n)=fordiv(n, d, my(m=n/d, k=d+n); if(Mod(d, k)^d==-n && Mod(d, k)^n==-d && Mod(n, k)^d==-d, return(0))); 1 \\ Charles R Greathouse IV, Feb 19 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Juri-Stepan Gerasimov, Feb 07 2015
STATUS
approved