A260581 - OEIS

%I #21 Apr 28 2017 15:15:49

%S 1,2,7,8,9,13,14,18,19,23,25,26,31,37,38,40,43,46,47,49,50,53,61,62,

%T 67,73,74,77,79,80,83,86,88,89,94,95,97,98,99,103,104,106,108,109,113,

%U 121,122,124,127,131,132,134,136,139,143,146,148,151,152,154,156

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

%C 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.

%H Peter J. C. Moses, <a href="/A260581/b260581.txt">Table of n, a(n) for n = 1..2000</a>

%e 8 is in the sequence since d(8+d(8)) = d(12)= 6 > d(8) = 4.

%t Select[Range@156,DivisorSigma[0,#+DivisorSigma[0,#]]>DivisorSigma[0,#]&] (* _Ivan N. Ianakiev_, Aug 13 2015 *)

%o (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

%o (Perl) use ntheory ":all"; my @A = grep { my $d=scalar(divisors($_)); scalar(divisors($_+$d)) > $d; } 1..100; say "@A"; # _Dana Jacobsen_, Apr 28 2017

%Y Cf. A000005, A175304, A260577.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Jul 29 2015