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

Author

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

Keywords

• hard
• nonn
• nice
• more

Comments

Invented by the HR concept formation program.

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

Examples

			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 ].
		

Links

• S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
• S. Colton, HR - Automatic Theory Formation in Pure Mathematics

Crossrefs

Cf. A036431.

Programs

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

Formula

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

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