A325094 Write n as a sum of distinct powers of 2, then take the primes of those powers of 2 and multiply them together.

1, 2, 3, 6, 7, 14, 21, 42, 19, 38, 57, 114, 133, 266, 399, 798, 53, 106, 159, 318, 371, 742, 1113, 2226, 1007, 2014, 3021, 6042, 7049, 14098, 21147, 42294, 131, 262, 393, 786, 917, 1834, 2751, 5502, 2489, 4978, 7467, 14934, 17423, 34846, 52269, 104538, 6943

Offset

0,2

Comments

The sorted sequence is A325093.

For example, 11 = 1 + 2 + 8, so a(11) = prime(1) * prime(2) * prime(8) = 114.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Example

The sequence of terms together with their prime indices begins:
    1: {}
    2: {1}
    3: {2}
    6: {1,2}
    7: {4}
   14: {1,4}
   21: {2,4}
   42: {1,2,4}
   19: {8}
   38: {1,8}
   57: {2,8}
  114: {1,2,8}
  133: {4,8}
  266: {1,4,8}
  399: {2,4,8}
  798: {1,2,4,8}
   53: {16}
  106: {1,16}
  159: {2,16}
  318: {1,2,16}
  371: {4,16}

Maple

P:= [seq(ithprime(2^i), i=0..10)]:
f:= proc(n) local L, i;
  L:= convert(n, base, 2);
  mul(P[i]^L[i], i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, Mar 28 2019

Mathematica

Table[Times@@MapIndexed[If[#1==0, 1, Prime[2^(#2[[1]]-1)]]&, Reverse[IntegerDigits[n, 2]]], {n, 0, 100}]

Crossrefs

Cf. A000720, A001222, A005117, A018819, A019565, A033844, A056239, A102378, A112798, A247935, A318400.

Cf. A325091, A325092, A325093, A325106.

Sequence in context: A349756 A018748 A018258 * A191614 A018379 A245479

Adjacent sequences: A325091 A325092 A325093 * A325095 A325096 A325097

Keyword

nonn,look

Author

Gus Wiseman, Mar 27 2019

Status

approved