A326952 a(n) = A001222(A028905(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 2, 2, 1, 1, 1, 5, 1, 1, 1, 1, 1, 3, 3, 1, 3, 1, 1, 1, 7, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 3, 2, 2, 1, 4, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 2

Offset: 1

Author

Joshua Michael McAteer, Aug 06 2019

Keywords

• nonn
• base

Comments

Multiplicity of prime divisors of n, where n is a number composed of the sorted digits of a prime number.

Conjecture: the sum of the first n terms of A326952 (smallest to largest sorting) is <= the sum of the first n terms of A326953 (largest to smallest sorting). This is true for the first 9592 terms.

Examples

			The 13th prime number is 41. Sorting the digits gives 14. 14 has 2 factors, 2 and 7. The 13th term of this sequence is 2.
		

Links

• Joshua Michael McAteer, Table of n, a(n) for n = 1..9592

Crossrefs

Cf. A001222 (bigomega), A028905, A326953 (for reverse sorting).

Programs

MATLAB

nmax= 100;
p = primes(nmax);
lp = length(p);
sfac = zeros(1,lp);
for i = 1:lp
digp=str2double(regexp(num2str(p(i)),'\d','match'));
sdigp = sort(digp);
l=length(digp);
conv = 10.^flip(0:(l-1));
snum = sum(conv.*sdigp);
sfac(i) = numel(factor(snum));
end