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A303695
a(n) is the sum of divisors d of n such that bigomega(d) is a divisor of bigomega(n) where bigomega(x) is A001222(x), the number of prime divisors of x counted with multiplicity.
1
1, 2, 3, 6, 5, 11, 7, 10, 12, 17, 11, 17, 13, 23, 23, 22, 17, 23, 19, 27, 31, 35, 23, 39, 30, 41, 30, 37, 29, 40, 31, 34, 47, 53, 47, 60, 37, 59, 55, 61, 41, 54, 43, 57, 53, 71, 47, 53, 56, 57, 71, 67, 53, 74, 71, 83
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
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
Sequence in context: A319680 A350337 A133477 * A345321 A350339 A039653
KEYWORD
nonn
AUTHOR
Lechoslaw Ratajczak, Jul 03 2018
EXTENSIONS
Name edited by Michel Marcus, Jul 05 2018
STATUS
approved