login
Write n as a sum of distinct powers of 2, then take the primes of those powers of 2 and multiply them together.
8

%I #10 Mar 28 2019 12:13:46

%S 1,2,3,6,7,14,21,42,19,38,57,114,133,266,399,798,53,106,159,318,371,

%T 742,1113,2226,1007,2014,3021,6042,7049,14098,21147,42294,131,262,393,

%U 786,917,1834,2751,5502,2489,4978,7467,14934,17423,34846,52269,104538,6943

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

%C The sorted sequence is A325093.

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

%H Robert Israel, <a href="/A325094/b325094.txt">Table of n, a(n) for n = 0..10000</a>

%e The sequence of terms together with their prime indices begins:

%e 1: {}

%e 2: {1}

%e 3: {2}

%e 6: {1,2}

%e 7: {4}

%e 14: {1,4}

%e 21: {2,4}

%e 42: {1,2,4}

%e 19: {8}

%e 38: {1,8}

%e 57: {2,8}

%e 114: {1,2,8}

%e 133: {4,8}

%e 266: {1,4,8}

%e 399: {2,4,8}

%e 798: {1,2,4,8}

%e 53: {16}

%e 106: {1,16}

%e 159: {2,16}

%e 318: {1,2,16}

%e 371: {4,16}

%p P:= [seq(ithprime(2^i),i=0..10)]:

%p f:= proc(n) local L,i;

%p L:= convert(n,base,2);

%p mul(P[i]^L[i],i=1..nops(L))

%p end proc:

%p map(f, [$0..100]); # _Robert Israel_, Mar 28 2019

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

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

%Y Cf. A325091, A325092, A325093, A325106.

%K nonn,look

%O 0,2

%A _Gus Wiseman_, Mar 27 2019