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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Feb 03 2022

Keywords

• nonn
• base
• easy

Comments

See also comments in A143293.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base

Crossrefs

Cf. A002110, A051903, A276156, A143293.

Programs

Mathematica

{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 *)

PARI

A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
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); };
A351073(n) = A051903(A276156(n));

Formula

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

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