OFFSET
1,3
FORMULA
For n!=4: a(n)=(p_1*p_2*...p_r)^n/n-n*(n-1)/2 with prime factorization n=p_1^b_1*...*p_r^b_r.
Proof of formula: If a is the first member in A.P. then there must exist an integer m with n*a+n*n*(n-1)/2=m^n. Therefore all prime divisors of n divide m. For n>4 this gives a positive solution for a.
EXAMPLE
a(4) = 58 and 58 +62 +66 +70 = 256 = 4^4.
MAPLE
for n from 1 to 50 do a := ifactors(n); b := 1:for j from 1 to nops(a[2]) do b := b*a[2][j][1]; od; c[n] := b^n/n-n*(n-1)/2; od:c[4] := 58:seq(c[j], j=1..50);
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Aug 14 2002
EXTENSIONS
Formula and more terms from Sascha Kurz, Aug 14 2002
STATUS
approved