A036432 Sets a record for the number of positive integers which, when added to the number of their divisors, gives n.

1, 2, 7, 38, 122, 2766, 64686, 1972296, 5387768, 56208248, 753815160, 130065181784, 5398921735160

Offset

0,2

Comments

Invented by the HR concept formation program.

a(13) > 10^13. - Giovanni Resta, Feb 24 2020

Links

Table of n, a(n) for n=0..12.

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

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

Formula

Sets record for |{b in N : b + tau(b) = n}|.

Example

1 [ first with 0 ].
2=1+tau(1) [ first with 1 ].
7=4+tau(4) and 5+tau(5) [ first with 2 ].
38=30+tau(30) and 32+tau(32) and 34+tau(34) [ first with 3 ].

Prog

(PARI) nbi(n) = {nb = 0; for (i = 1, n, if ((i + numdiv(i)) == n, nb++); ); nb; }
lista(nn) = {rec = -1; for (n = 1, nn, new = nbi(n); if (new > rec, print1(n, ", "); rec = new; ); ); } \\ Michel Marcus, Aug 31 2013

Crossrefs

Cf. A036431.

Sequence in context: A182331 A173762 A180269 * A275621 A094431 A256032

Adjacent sequences: A036429 A036430 A036431 * A036433 A036434 A036435

Keyword

hard,nonn,nice,more

Author

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

Extensions

More terms from Julian Richardson (julianr(AT)dai.ed.ac.uk), who has searched up to 100000000.

a(10)-a(11) from Donovan Johnson, Feb 19 2009

a(12) from Giovanni Resta, Feb 24 2020

Status

approved