OFFSET
1,1
COMMENTS
This sequence appears to be identical to A073582 with its first term omitted and to A161344 with its first two terms omitted.
Conjectures. (1) If m>=14 is a term of this sequence, then sigma(2,m) is congruent to 5 + m/2 modulo m; (2) If m>=22 is a term of this sequence, then sigma(3,m) is congruent to 9 + m/2 modulo m; If m>=38 is a term of this sequence, then sigma(4,m) is congruent to 17 + m/2 modulo m. (sigma(k,m) denotes the sum of the k-th powers of the divisors of m.)
Similar conjectures can be made about sigma(k,m) congruent to 2^k+1 + m/2 modulo m, for m a sufficiently large term of this sequence..
The even semiprimes (A100484) m= 2*p with p>3, with sigma(2*p)= 3+p (mod 2p), are a subsequence. - R. J. Mathar, Oct 02 2011
The terms in this sequence which are not even semiprimes are 8, 690, 12978, 176946, ... - R. J. Mathar, Aug 24 2023
MAPLE
isA196226 := proc(n)
sigmar := modp(numtheory[sigma](n), n) ;
if sigmar = 3+n/2 then
true;
else
false;
end if;
end proc:
A196226 := proc(n)
option remember;
if n =1 then
8;
else
for a from procname(n-1)+1 do
if isA196226(a) then
return a;
end if;
end do:
end if;
end proc:
seq(A196226(n), n=1..100) ; # R. J. Mathar, Aug 24 2023
PROG
(PARI) lista(nn) = {for(n=1, nn, if ((sigma(n) % n) == (3 + n/2), print1(n, ", ")); ); } \\ Michel Marcus, Jul 12 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Sep 29 2011
STATUS
approved