cp's OEIS Frontend

A332222 a(n) = A156552(sigma(A005940(1+n))).

%I A332222 #9 Feb 13 2020 02:52:51
%S A332222 0,2,3,8,5,11,32,10,7,13,23,35,1024,66,39,1024,11,23,31,37,47,55,133,
%T A332222 43,258,2050,4099,72,267,87,48,38,17,27,47,71,55,95,263,45,95,111,191,
%U A332222 151,8199,269,175,4099,264,518,1035,2056,1037,8203,2080,138,207,539,1071,167,1048592,98,291,1073741824,13,37,71,75,75,111
%N A332222 a(n) = A156552(sigma(A005940(1+n))).
%H A332222 Antti Karttunen, <a href="/A332222/b332222.txt">Table of n, a(n) for n = 0..479</a>
%H A332222 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A332222 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A332222 a(n) = A156552(A000203(A005940(1+n))).
%F A332222 a(n) = A332221(A005940(1+n)) = A156552(A324054(n)).
%t A332222 Array[Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ DivisorSigma[1, #]]] &@ Block[{p = Partition[Split[Join[IntegerDigits[#, 2], {2}]], 2], q}, Times @@ Flatten[Table[q = Take[p, -i]; Prime[Count[Flatten[q], 0] + 1]^q[[1, 1]], {i, Length[p]}]]] &, 70, 0] (* _Michael De Vlieger_, Feb 12 2020, after _Robert G. Wilson v_ at A005940 *)
%o A332222 (PARI)
%o A332222 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A332222 A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A332222 A332222(n) = A156552(sigma(A005940(1+n)));
%Y A332222 Cf. A000203, A005940, A156552, A324054, A332221.
%Y A332222 Cf. also A332223.
%K A332222 nonn
%O A332222 0,2
%A A332222 _Antti Karttunen_, Feb 12 2020