OFFSET
1,2
COMMENTS
For p prime, p^p satisfy the condition, hence A051674 (and also A048102) is a subsequence. Moreover, if p and q are primes and i and j are positive integers, if p^i * q^j verify the condition, then the same is true for p^j * q^i. So A122406 is also a subsequence. More generally, if a number is a term, then any permutation of the exponents in its prime factorization (i.e. any permutation of its prime signature) gives also a term. In addition, any number having no more than two distinct prime factors (apart their multiplicity) is a term iff it belongs also to A272858.
LINKS
Giuseppe Coppoletta and Giovanni Resta, Table of n, a(n) for n = 1..1413 (terms < 10^19, first 100 terms from G. Coppoletta)
EXAMPLE
885735 = 3^11 * 5 is included because (3+5) + 3*5 = (11+1) + 11*1.
2^10 * 3^6 * 19^2 is included because (2+3+19)+ 2*3*19 = (10+6+2)+ 10*6*2.
MATHEMATICA
Select[Range[10^6], Total@ First@ # + Times @@ First@ # == Total@ Last@ # + Times @@ Last@ # &@ Transpose@ FactorInteger@ # &] (* Michael De Vlieger, May 08 2016 *)
PROG
(Sage)
def d(n):
v = factor(n)
d1 = sum(w[0] for w in v) + prod(w[0] for w in v)
d2 = sum(w[1] for w in v) + prod(w[1] for w in v)
return d1 == d2
[k for k in (1..10000) if d(k)]
(PARI) spp(v) = vecsum(v) + prod(k=1, #v, v[k]);
isok(n) = my(f = factor(n)); spp(f[, 1]) == spp(f[, 2]); \\ Michel Marcus, May 08 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Giuseppe Coppoletta, May 08 2016
STATUS
approved