

A191161


Hypersigma(n), definition 2: sum of the divisors of n plus the recursive sum of the divisors of the proper divisors.


3



1, 4, 5, 12, 7, 22, 9, 32, 19, 30, 13, 72, 15, 38, 37, 80, 19, 90, 21, 96, 47, 54, 25, 208, 39, 62, 65, 120, 31, 178, 33, 192, 67, 78, 65, 316, 39, 86, 77, 272, 43, 222, 45, 168, 147, 102, 49, 560, 67, 174, 97, 192, 55
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OFFSET

1,2


COMMENTS

In wanting to ensure the definition was not arbitrary, I initially thought that 1s had to stop the recursion. But as T. D. Noe showed me, this doesn't have to be the case: the 1s can be included in the recursion.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = sigma(n) + sum_{d  n, d < n} a(d). [Charles R Greathouse IV, Dec 20 2011]


MATHEMATICA

hsTD[n_] := hsTD[n] = Module[{d = Divisors[n]}, Total[d] + Total[hsTD /@ Most[d]]]; Table[hsTD[n], {n, 100}] (* From T. D. Noe *)


PROG

(PARI) a(n)=sumdiv(n, d, if(d<n, d+a(d), n)) \\ Charles R Greathouse IV, Dec 20 2011


CROSSREFS

Cf. A000203, A191150.
Sequence in context: A260624 A067371 A068719 * A246316 A034773 A323766
Adjacent sequences: A191158 A191159 A191160 * A191162 A191163 A191164


KEYWORD

nonn,easy


AUTHOR

Alonso del Arte, May 26 2011


STATUS

approved



