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A036431 a(n) = number of positive integers b which, when added to the number of their divisors, tau(b), gives n. 2
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 (list; graph; refs; listen; history; text; internal format)
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) = {nb = 0; for (i = 1, n, if ((i + numdiv(i)) == n, nb++); ); nb; } \\ Michel Marcus, Aug 31 2013

CROSSREFS

Cf. A036432.

Sequence in context: A140080 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

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)