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A178344 a(n) = Sum_i prime(i+1)^b(i) where n = Sum_{i>=0} b(i)*2^e(i) is the binary representation of n.

%I A178344 #16 Feb 19 2019 23:14:42
%S A178344 1,2,4,5,7,8,9,10,10,11,12,13,14,15,16,17,15,16,17,18,19,20,21,22,21,
%T A178344 22,23,24,25,26,27,28,18,19,20,21,22,23,24,25,24,25,26,27,28,29,30,31,
%U A178344 28,29,30,31,32,33,34,35,34,35,36,37,38,39,40,41,23,24,25,26,27,28,29,30,29,30
%N A178344 a(n) = Sum_i prime(i+1)^b(i) where n = Sum_{i>=0} b(i)*2^e(i) is the binary representation of n.
%C A178344 a(0) = 0 might be a more logical value for the initial term. - _Antti Karttunen_, Sep 28 2018
%H A178344 Antti Karttunen, <a href="/A178344/b178344.txt">Table of n, a(n) for n = 0..65537</a>
%F A178344 For n >= 1, a(n) = A089625(n) + A080791(n). - _Antti Karttunen_, Sep 28 2018
%e A178344 a(16)=15 because 10000 is the base-2 representation of n=16 and 11^1 + 7^0 + 5^0 + 3^0 + 2^0 = 15.
%p A178344 A178344 := proc(n)
%p A178344     if n = 0 then
%p A178344         dgs := [0] ;
%p A178344     else
%p A178344         dgs := convert(n,base,2) ;
%p A178344     end if;
%p A178344     add(ithprime(i)^dgs[i],i=1..nops(dgs)) ;
%p A178344 end proc:
%p A178344 seq(A178344(n),n=0..73) ; # _R. J. Mathar_, Sep 28 2018
%t A178344 Array[Total@ MapIndexed[Prime[First@ #2]^#1 &, Reverse@ IntegerDigits[#, 2]] &, 74, 0] (* _Michael De Vlieger_, Feb 19 2019 *)
%o A178344 (PARI) a(n) = my(b=Vecrev(binary(n))); if (n==0, b=[0]); sum(i=1, #b, prime(i)^b[i]); \\ _Michel Marcus_, Sep 29 2018
%Y A178344 Cf. A000040, A001477, A056791, A007088, A080791, A089625, A143710, A175524.
%Y A178344 Cf. A178562 (first differences).
%K A178344 nonn,base
%O A178344 0,2
%A A178344 _Juri-Stepan Gerasimov_, May 25 2010, Jan 06 2010
%E A178344 Offset modified, keyword:base added by _R. J. Mathar_, May 28 2010