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A239283
n^(p1) + n^(p2) + n^(p3) + ... where (p1)*(p2)*(p3)*.... is the prime factorization of n (with multiplicity).
1
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
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 A372487 A274854
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 14 2014
STATUS
approved