OFFSET
1,2
COMMENTS
a(n) < sigma(n) (for n>1).
The least nonprime solution m of the equation m^2 mod (a(m^2) - m^2) = 0 is 18. What is the next nonprime solution of this equation? If it exists, it is greater than 10^6.
No other such terms up to 10^7. - Michel Marcus, Jul 05 2018
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
EXAMPLE
a(24) = 39 because: 24 = (2^3)*(3^1) (bigomega(24) = 4) and (2^0)*(3^1) = 3 ((0+1)|4), (2^1)*(3^0) = 2 ((1+0)|4), (2^1)*(3^1) = 6 ((1+1)|4), (2^2)*(3^0) = 4 ((2+0)|4), (2^3)*(3^1) = 24 ((3+1)|4), hence 3+2+6+4+24 = 39
MATHEMATICA
{1}~Join~Table[Total@Select[Divisors[n], PrimeOmega[#] > 0 && Divisible[PrimeOmega[n], PrimeOmega[#]] &], {n, 2, 56}] (* Ivan Neretin, Jun 20 2019 *)
PROG
(PARI) a(n) = if (n==1, 1, my(b=bigomega(n)); sumdiv(n, d, if (d != 1, d*((b % bigomega(d)) == 0)))); \\ Michel Marcus, Jul 03 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Lechoslaw Ratajczak, Jul 03 2018
EXTENSIONS
Name edited by Michel Marcus, Jul 05 2018
STATUS
approved