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A191150 Hypersigma(n): sum of the divisors of n plus the recursive sum of the divisors of the restricted divisors 4
1, 3, 4, 10, 6, 19, 8, 28, 17, 27, 12, 64, 14, 35, 34, 72, 18, 82, 20, 88, 44, 51, 24, 188, 37, 59, 61, 112, 30, 165, 32, 176, 64, 75, 62, 290, 38, 83, 74, 252, 42, 209, 44, 160, 139, 99, 48, 512, 65, 166, 94, 184, 54 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First we add up all the divisors of n, and then we add in the divisors of each restricted divisor of n (not 1 or n itself) and continue the recursion until such a depth as that there only numbers with no restricted divisors (prime numbers).

Thus if n is prime then hypersigma(n) is the same as sigma(n).

LINKS

Alonso del Arte, Table of n, a(n) for n = 1..1000

EXAMPLE

a(12) = 64 since: the sum of the divisors of 12 is 28; to 28 we add 3 and 4 (corresponding to the prime divisors 2 and 3) bringing us up to 35; for 4 and 6 we continue the recursion, with 4 bringing us up to 45 and 6 brings up to 64.

MAPLE

with(numtheory);

P:=proc(n)

local b, c, k, s;

s:=sigma(n); b:=nops(divisors(n)); c:=(sort([op(divisors(n))]));

for k from 2 to b-1 do

  if isprime(c[k]) then s:=s+c[k]+1;

  else

     s:=s+P(c[k]);

  fi;

od;

s;

end:

hps:=proc(i)

local n;

for n from 1 to i do print(P(n)); od;

end:

hps(100);   # Paolo P. Lava, Jul 13 2011

MATHEMATICA

hyperSigma[1] := 1; hyperSigma[n_] := hyperSigma[n] = Module[{d=Divisors[n]}, Total[d] + Total[hyperSigma /@ Rest[Most[d]]]]; Table[hyperSigma[n], {n, 100}] (* From T. D. Noe with a slight modification *)

CROSSREFS

Cf. A000203.

Sequence in context: A247372 A143443 A139556 * A023896 A328711 A222136

Adjacent sequences:  A191147 A191148 A191149 * A191151 A191152 A191153

KEYWORD

nonn,easy

AUTHOR

Alonso del Arte, May 26 2011

EXTENSIONS

Example corrected by Paolo P. Lava, Jul 13 2011

STATUS

approved

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Last modified January 23 22:16 EST 2020. Contains 331177 sequences. (Running on oeis4.)