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

0, 2, 3, 8, 5, 11, 32, 10, 7, 13, 23, 35, 1024, 66, 39, 1024, 11, 23, 31, 37, 47, 55, 133, 43, 258, 2050, 4099, 72, 267, 87, 48, 38, 17, 27, 47, 71, 55, 95, 263, 45, 95, 111, 191, 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

Offset: 0

Author

Antti Karttunen, Feb 12 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..479
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A005940, A156552, A324054, A332221.

Cf. also A332223.

Programs

Mathematica

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 *)

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
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
A332222(n) = A156552(sigma(A005940(1+n)));

Formula

a(n) = A156552(A000203(A005940(1+n))).

a(n) = A332221(A005940(1+n)) = A156552(A324054(n)).