OFFSET
1,2
COMMENTS
Complement to the union of A175304 and A260577. All primes and their squares, except for 4 and the smaller members of pairs of twin primes (A001359), are in the sequence. If odd prime p is not the smaller member of a twin pair, then 2*p is in the sequence; if for prime p, 2*p+3 is neither prime nor square of prime, then 4*p is in the sequence; for prime p>7, 8*p is in the sequence; for every prime p, 2*p^2 is always in the sequence.
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..2000
EXAMPLE
8 is in the sequence since d(8+d(8)) = d(12)= 6 > d(8) = 4.
MATHEMATICA
Select[Range@156, DivisorSigma[0, #+DivisorSigma[0, #]]>DivisorSigma[0, #]&] (* Ivan N. Ianakiev, Aug 13 2015 *)
PROG
(PARI) first(m)=my(v=vector(m), r=1); for(i=1, m, while(!(numdiv(r+numdiv(r)) > numdiv(r)), r++); v[i]=r; r++; ); v; \\ Anders Hellström, Aug 16 2015
(Perl) use ntheory ":all"; my @A = grep { my $d=scalar(divisors($_)); scalar(divisors($_+$d)) > $d; } 1..100; say "@A"; # Dana Jacobsen, Apr 28 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jul 29 2015
STATUS
approved