

A351775


Value of all prime numbers p after applying the rule: sigma_n( sigma_n1( ... sigma_3( sigma_2( sigma_1( sigma_0(p) )))...)) (from sigma_0 up to sigma_n), where sigma_k(m) is the sum of the kth powers of the divisors of m and p is prime (the choice of the prime p is arbitrary).


0




OFFSET

0,1


COMMENTS

a(6) has 368 digits.


LINKS



FORMULA

a(n) = sigma_n( a(n1) ) for n >= 1, a(0) = 2.


EXAMPLE

a(0) = sigma_0(2) = 2,
a(1) = sigma_1( sigma_0(2) ) = 3,
a(2) = sigma_2( sigma_1( sigma_0(2) )) = sigma_2(3) = 10,
a(3) = sigma_3( sigma_2( sigma_1( sigma_0(2) ))) = sigma_3(10) = 1134.
...


MATHEMATICA

a[0] = 2; a[n_] := a[n] = DivisorSigma[n, a[n  1]]; Table[a[n], {n, 0, 6}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



