A351775 Value of all prime numbers p after applying the rule: sigma_n( sigma_n-1( ... 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 k-th powers of the divisors of m and p is prime (the choice of the prime p is arbitrary).

2, 3, 10, 1134, 1779741927370, 18420061471485119632756156593998809036909505674991629417779936

Offset

0,1

Comments

a(6) has 368 digits.

Links

Table of n, a(n) for n=0..5.

Formula

a(n) = sigma_n( a(n-1) ) 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

Cf. A070239.

Sequence in context: A184163 A218271 A128125 * A070239 A002443 A111788

Adjacent sequences: A351772 A351773 A351774 * A351776 A351777 A351778

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 18 2022

Status

approved