A326953 a(n) = A001222(A028906(n)).

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

Offset

1,8

Comments

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

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

Links

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

Example

The 28th prime number is 107. The reverse sorted digits are 710. The factorization of 710 is 2, 5, 71, therefore the 28th term in this sequence is 3.

Prog

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

Crossrefs

Cf. A001222 (bigomega), A028906, A326952 (for ascending sorted version).

Sequence in context: A265318 A279536 A269954 * A234255 A062706 A059217

Adjacent sequences: A326950 A326951 A326952 * A326954 A326955 A326956

Keyword

nonn,base

Author

Joshua Michael McAteer, Aug 06 2019

Status

approved