A290703 Solutions to x + d(x) = sigma(x)/2, where d(x) is the number of divisors of x.

176, 2205, 7544, 10184, 28544, 503296, 1020568, 2051072, 6019264, 10001848, 15317696, 35019968, 354375344, 535871488, 9175990784, 115917884416, 1520995423616, 1568751464576, 1627889399936, 16470699157376, 18150630940672, 300004994652928, 338107574312576

Offset

1,1

Links

Max Alekseyev, Table of n, a(n) for n = 1..41

Example

d(176) = 10, sigma(176) = 372 and 176 + 10 = 186 = 372/2.

Maple

with(numtheory): P:=proc(q) local n; for n from 1 to q do if
n+tau(n)=sigma(n)/2 then print(n); fi; od; end: P(10^9);

Mathematica

Select[Range[10^7], # + DivisorSigma[0, #] == DivisorSigma[1, #]/2 &] (* Michael De Vlieger, Aug 26 2017 *)

Prog

(PARI) isok(x) = x + numdiv(x) == sigma(x)/2; \\ Michel Marcus, Aug 25 2017

Crossrefs

Cf. A000005, A063788, A066229, A066230, A083874, A099650, A111592, A290704, A304276.

Sequence in context: A133063 A264892 A223611 * A077742 A027483 A243647

Adjacent sequences: A290700 A290701 A290702 * A290704 A290705 A290706

Keyword

nonn

Author

Paolo P. Lava, Aug 09 2017

Extensions

a(11)-a(12) from Michel Marcus, Aug 25 2017

a(13)-a(16) from Giovanni Resta, Aug 25 2017

Term a(17) onward from Max Alekseyev, Sep 23 2025

Status

approved