A274118 (1+e)-sigma betrothed numbers.

108, 140, 195, 1050, 1925, 8892, 16587, 312620, 549219, 587460, 1057595, 1279950, 2576945, 5088650, 6446325, 7460004, 7875450, 10925915, 13922100, 16381925, 22559060, 26502315, 29864120, 30809415, 31213899, 41137620, 84854315, 89446860, 102019644, 114859884

Offset

1,1

Comments

Members of a pair (m,n) such that (1+e)-sigma(m)=(1+e)-sigma(n)=m+n+1, where (1+e)-sigma = A051378.

So far, 108 is the only fixed point of the transform n -> (1+e)sigma(n)-n-1.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..50

Example

(1+e)-sigma(140) - 140 - 1 = 336 - 140 - 1 = 195 and (1+e)-sigma(195) - 195 - 1 = 336 - 195 - 1 = 140.

Maple

with(numtheory): T:=proc(n) local a, d, p, e, s, sp; a:=1;
for d in ifactors(n)[2] do p:=op(1, d); e:= op(2, d); sp:=1;
for s in divisors(e) do sp:=sp+p^s; od: a:=a*sp; od: a; end:
P:=proc(q) local n, x, y; for n from 2 to q do x:=T(n)-n-1; y:=T(x)-x-1;
if n=y then print(n); fi; od; end: P(10^10);

Crossrefs

Cf. A049603, A051378, A274116.

Sequence in context: A217541 A070797 A173748 * A046294 A039601 A330851

Adjacent sequences: A274115 A274116 A274117 * A274119 A274120 A274121

Keyword

nonn

Author

Paolo P. Lava, Jun 10 2016

Status

approved