A036431 a(n) = number of positive integers b which, when added to the number of their divisors, tau(b), gives n.

0, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 1, 3, 2, 0, 0, 1, 2, 0, 2, 0, 0, 1, 1, 3, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 2, 1, 1, 0, 1, 0, 0, 3, 0, 1, 1, 2, 2, 1, 0, 0, 2, 0, 0, 3, 1, 0, 1, 1, 3, 0, 0, 1, 2, 2, 0, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 1, 1, 2

Offset

1,7

Comments

Invented by the HR concept formation program.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.

S. Colton, HR - Automatic Theory Formation in Pure Mathematics

Formula

a(n) = |{b in N : b + tau(b) = n}|

Example

a(7) = 2 because (i) 4+tau(4)=7 and (ii) 5+tau(5)=7.

Maple

N:= 200: # to get a(1)..a(N)
A:= Vector(N):
for b from 1 to N do
  v:= b + numtheory:-tau(b);
  if v <= N then A[v]:= A[v]+1 fi
od:
convert(A, list); # Robert Israel, Jun 10 2018

Prog

(PARI) a(n) = sum(i=1, n, i+numdiv(i) == n); \\ Michel Marcus, Oct 01 2021

Crossrefs

Cf. A036432.

Sequence in context: A345927 A065359 A087372 * A029407 A259285 A099544

Adjacent sequences: A036428 A036429 A036430 * A036432 A036433 A036434

Keyword

nonn

Author

Simon Colton (simonco(AT)cs.york.ac.uk)

Extensions

a(87)=0 corrected by Michel Marcus, Aug 31 2013

Status

approved