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

1,6

Comments

See also comments in A143293.

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

Formula

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

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

Example

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.

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 *)

Prog

(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));

Crossrefs

Cf. A002110, A051903, A276156, A143293.

Sequence in context: A259341 A369589 A350733 * A046225 A269233 A123396

Adjacent sequences: A351070 A351071 A351072 * A351074 A351075 A351076

Keyword

nonn,base,easy

Author

Antti Karttunen, Feb 03 2022

Status

approved