

A196226


m such that A054024(m) (sum of divisors of m reduced modulo m) is 3 + m/2.


2



8, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 kth 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


LINKS



MAPLE

isA196226 := proc(n)
sigmar := modp(numtheory[sigma](n), n) ;
if sigmar = 3+n/2 then
true;
else
false;
end if;
end proc:
option remember;
if n =1 then
8;
else
for a from procname(n1)+1 do
if isA196226(a) then
return a;
end if;
end do:
end if;
end proc:


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



STATUS

approved



