A260581 Numbers n for which d(n+d(n)) > d(n), where d(n) is the number of divisors of n.

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

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

Cf. A000005, A175304, A260577.

Sequence in context: A270804 A167457 A287515 * A179772 A047354 A037455

Adjacent sequences: A260578 A260579 A260580 * A260582 A260583 A260584

Keyword

nonn

Author

Vladimir Shevelev, Jul 29 2015

Status

approved