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

Author

Gus Wiseman, Mar 27 2019

Keywords

• nonn
• look

Comments

The sorted sequence is A325093.

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

Examples

			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}
		

Links

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

Crossrefs

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

Cf. A325091, A325092, A325093, A325106.

Programs

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}]