A239283 n^(p1) + n^(p2) + n^(p3) + ... where (p1)*(p2)*(p3)*.... is the prime factorization of n (with multiplicity).

0, 4, 27, 32, 3125, 252, 823543, 192, 1458, 100100, 285311670611, 2016, 302875106592253, 105413700, 762750, 1024, 827240261886336764177, 11988, 1978419655660313589123979, 3200800, 1801097802, 584318301411812, 20880467999847912034355032910567, 15552, 19531250

Offset

1,2

Comments

The definition of the terms swaps the roles of the primes in the base and their exponents of A082872.

Contains A051674 as a subsequence at the prime positions n= 2, 3, 5, 7,.... Michel Marcus, Mar 14 2014

Links

Table of n, a(n) for n=1..25.

Formula

a(n) = sum_i [e_i*n^(p_i)], where n=product_i (p_i)^(e_i) is the prime factorization of n.

Example

a(8) = a(2*2*2) = 8^2 + 8^2 + 8^2 = 192.

Maple

A239283 := proc(n)
    local ps;
    ps := ifactors(n)[2] ;
    add( op(2, p)*n^op(1, p), p=ps) ;
end proc:
seq(A239283(n), n=1..22) ;

Prog

(PARI) a(n) = my(f = factor(n)); sum(i=1, #f~, f[i, 2]*n^f[i, 1]); \\ Michel Marcus, Mar 14 2014

Crossrefs

Sequence in context: A085702 A068349 A129204 * A082872 A274854 A054411

Adjacent sequences: A239280 A239281 A239282 * A239284 A239285 A239286

Keyword

nonn,easy

Author

R. J. Mathar, Mar 14 2014

Status

approved