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A079124 Number of ways to partition n into distinct positive integers <= phi(n), where phi is Euler's totient function (A000010). 7
1, 1, 0, 1, 0, 2, 0, 4, 1, 5, 1, 11, 0, 17, 4, 13, 13, 37, 2, 53, 13, 51, 35, 103, 10, 135, 78, 167, 89, 255, 4, 339, 253, 378, 306, 542, 121, 759, 558, 872, 498, 1259, 121, 1609, 1180, 1677, 1665, 2589, 808, 3250, 1969, 3844, 3325, 5119, 1850, 6268, 4758, 7546, 7070 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem, Mathematics and Computer Education, Vol. 31, No. 1, pp. 24-28, Winter 1997.  MathEduc Database (Zentralblatt MATH, 1997c.01891).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem II, Missouri Journal of Mathematical Sciences, Vol. 16, No. 1, Winter 2004, pp. 12-17. Zentralblatt MATH, Zbl 1071.05501.

FORMULA

a(n) = b(0, n), b(m, n) = 1 + sum(b(i, j): m<i<j<phi(n) & i+j=n).

MAPLE

with(numtheory):

b:= proc(n, i) option remember; `if`(n=0, 1,

      `if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, b(n-i, i-1))))

    end:

a:= n-> b(n, phi(n)):

seq(a(n), n=0..100);  # Alois P. Heinz, May 11 2015

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, b[n-i, i-1]]]]; a[n_] := b[n, EulerPhi[n]]; Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Jun 30 2015, after Alois P. Heinz *)

PROG

(Haskell)

a079124 n = p [1 .. a000010 n] n where

   p _      0 = 1

   p []     _ = 0

   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m

-- Reinhard Zumkeller, Jul 05 2013

CROSSREFS

Cf. A079126, A000009, A079122, A079125, A067953.

Cf. A227296, A036998.

Sequence in context: A020781 A327883 A007432 * A242071 A176910 A243981

Adjacent sequences:  A079121 A079122 A079123 * A079125 A079126 A079127

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 27 2002

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, May 11 2015

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)