login
A260581
Numbers n for which d(n+d(n)) > d(n), where d(n) is the number of divisors of n.
1
1, 2, 7, 8, 9, 13, 14, 18, 19, 23, 25, 26, 31, 37, 38, 40, 43, 46, 47, 49, 50, 53, 61, 62, 67, 73, 74, 77, 79, 80, 83, 86, 88, 89, 94, 95, 97, 98, 99, 103, 104, 106, 108, 109, 113, 121, 122, 124, 127, 131, 132, 134, 136, 139, 143, 146, 148, 151, 152, 154, 156
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
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