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A351073 Maximal exponent in the prime factorization of A276156(n).

%I A351073 #18 Feb 04 2022 20:41:32
%S A351073 0,1,1,1,1,3,2,1,1,5,1,2,1,1,1,1,1,2,1,3,1,1,1,4,1,2,5,1,1,3,1,1,1,3,
%T A351073 2,2,1,1,1,2,1,1,1,1,1,2,4,3,1,1,2,1,2,5,2,2,1,3,1,2,1,1,1,1,1,4,2,2,
%U A351073 2,1,1,2,1,1,1,1,1,2,2,5,1,1,1,2,1,3,2,1,1,6,1,2,1,1,1,2,1,1,1,3,1,2,1,1,1
%N A351073 Maximal exponent in the prime factorization of A276156(n).
%C A351073 See also comments in A143293.
%H A351073 Antti Karttunen, <a href="/A351073/b351073.txt">Table of n, a(n) for n = 1..65537</a>
%H A351073 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A351073 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A351073 a(n) = A051903(A276156(n)).
%F A351073 For n >= 1, a(2^n) = 1.
%e A351073 For n = 1040 = 2^10 + 2^4, A276156(n) = A002110(10) + A002110(4) = 6469693440 = 2^12 * 3 * 5 * 7^3 * 307. The largest exponent is 12, therefore a(1040) = 12.
%t A351073 {0}~Join~Array[Max[FactorInteger[#][[All, -1]]] &@ Total[Times @@@ Transpose@{Map[Times @@ # &, Prime@ Range@ Range[0, Length@ # - 1]], Reverse@ #}] &@ IntegerDigits[#, 2] &, 104, 2] (* _Michael De Vlieger_, Feb 04 2022 *)
%o A351073 (PARI)
%o A351073 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A351073 A276156(n) = { my(s=0, p=1, r=1); while(n, if(n%2, s += r); n>>=1; p = nextprime(1+p); r *= p); (s); };
%o A351073 A351073(n) = A051903(A276156(n));
%Y A351073 Cf. A002110, A051903, A276156, A143293.
%K A351073 nonn,base,easy
%O A351073 1,6
%A A351073 _Antti Karttunen_, Feb 03 2022