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Maximal exponent in the prime factorization of A276156(n).
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%I #18 Feb 04 2022 20:41:32

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

%C See also comments in A143293.

%H Antti Karttunen, <a href="/A351073/b351073.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = A051903(A276156(n)).

%F For n >= 1, a(2^n) = 1.

%e 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 {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 (PARI)

%o A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));

%o 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(n) = A051903(A276156(n));

%Y Cf. A002110, A051903, A276156, A143293.

%K nonn,base,easy

%O 1,6

%A _Antti Karttunen_, Feb 03 2022