A332221 a(n) = A156552(sigma(n)).

0, 2, 3, 8, 5, 11, 7, 10, 32, 13, 11, 35, 17, 23, 23, 1024, 13, 66, 19, 37, 31, 27, 23, 43, 1024, 37, 39, 71, 21, 55, 31, 38, 47, 29, 47, 72, 257, 43, 71, 45, 37, 95, 67, 75, 133, 55, 47, 4099, 258, 2050, 55, 49, 29, 87, 55, 87, 79, 45, 43, 151, 2049, 95, 263, 1073741824, 75, 111, 259, 77, 95, 111, 55, 138, 4097, 517, 4099, 83

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences related to sigma(n)

Formula

a(n) = A156552(A000203(n)).

A000120(a(n)) = A058063(n).

Mathematica

Array[Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ DivisorSigma[1, #]]] &, 76] (* Michael De Vlieger, Feb 12 2020 *)

Prog

(PARI)
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
A332221(n) = A156552(sigma(n));

Crossrefs

Cf. A000203, A156552, A058063, A332216 (fixed points), A332218, A332222.

Sequence in context: A126102 A011433 A349824 * A340393 A332222 A126139

Adjacent sequences: A332218 A332219 A332220 * A332222 A332223 A332224

Keyword

nonn

Author

Antti Karttunen, Feb 12 2020

Status

approved