cp's OEIS Frontend

A343416 a(n) = A001414(n) + A000203(n) + A001414(A000203(n)) + A000203(A001414(n)).

%I A343416 #11 Dec 23 2024 09:51:48
%S A343416 1,11,15,25,22,30,29,41,44,41,42,54,50,55,56,85,61,78,68,76,70,73,80,
%T A343416 94,90,93,73,92,99,112,105,104,97,104,99,139,134,125,116,126,137,149,
%U A343416 146,137,119,140,154,182,117,167,146,149,172,157,131,161,151,166,191,224,218,190,150,294,155,205
%N A343416 a(n) = A001414(n) + A000203(n) + A001414(A000203(n)) + A000203(A001414(n)).
%C A343416 If n = prime(k) is prime, a(n) = 3*prime(k)+1+A210934(k).
%H A343416 Robert Israel, <a href="/A343416/b343416.txt">Table of n, a(n) for n = 1..10000</a>
%e A343416 For n = 3, A001414(3) = 3, A000203(3) = A000203(A001414(3)) = 4 and A001414(A000203(3)) = 4, so a(3) = 3+4+4+4 = 15.
%p A343416 spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
%p A343416 f:= proc(n) local a,b;
%p A343416   a:= spf(n);
%p A343416   b:= numtheory:-sigma(n);
%p A343416   a+b+spf(b)+numtheory:-sigma(a)
%p A343416 end proc:
%p A343416 map(f, [$1..100]);
%Y A343416 Cf. A000203, A001414, A210934.
%K A343416 nonn
%O A343416 1,2
%A A343416 _J. M. Bergot_ and _Robert Israel_, Apr 14 2021