OFFSET
1,2
COMMENTS
Conjecture: for n>1, a(n) = n iff n is prime. Companion to A156833.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} phi(d) * binomial(d+n/d-2, d-1). - Seiichi Manyama, Apr 22 2021
G.f.: Sum_{k >= 1} phi(k) * (x/(1 - x^k))^k. - Seiichi Manyama, Apr 22 2021
EXAMPLE
a(4) = 5 = (1, 2, 0, 1) dot (1, 1, 2, 2) = (1 + 2 + 0 + 2), where row 4 of A156348 = (1, 2, 0, 1) and (1, 1, 2, 2) = the first 4 terms of Euler's phi function.
MAPLE
A156834 := proc(n)
add(A156348(n, k)*numtheory[phi](k), k=1..n) ;
end proc: # R. J. Mathar, Mar 03 2013
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[#] * Binomial[# + n/# - 2, #-1] &]; Array[a, 100] (* Amiram Eldar, Apr 22 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d)*binomial(d+n/d-2, d-1)); \\ Seiichi Manyama, Apr 22 2021
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*(x/(1-x^k))^k)) \\ Seiichi Manyama, Apr 22 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Feb 16 2009
EXTENSIONS
Extended beyond a(14) by R. J. Mathar, Mar 03 2013
STATUS
approved