login
n^(p1) + n^(p2) + n^(p3) + ... where (p1)*(p2)*(p3)*.... is the prime factorization of n (with multiplicity).
1

%I #13 Mar 14 2014 10:51:59

%S 0,4,27,32,3125,252,823543,192,1458,100100,285311670611,2016,

%T 302875106592253,105413700,762750,1024,827240261886336764177,11988,

%U 1978419655660313589123979,3200800,1801097802,584318301411812,20880467999847912034355032910567,15552,19531250

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

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

%C Contains A051674 as a subsequence at the prime positions n= 2, 3, 5, 7,.... _Michel Marcus_, Mar 14 2014

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

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

%p A239283 := proc(n)

%p local ps;

%p ps := ifactors(n)[2] ;

%p add( op(2,p)*n^op(1,p),p=ps) ;

%p end proc:

%p seq(A239283(n),n=1..22) ;

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

%K nonn,easy

%O 1,2

%A _R. J. Mathar_, Mar 14 2014