A260577 -id:A260577 - cp's OEIS frontend

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

Vladimir Shevelev, Jul 29 2015

nonn

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.

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

Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Cf. A000005, A175304, A260577.

Select[Range@156,DivisorSigma[0,#+DivisorSigma[0,#]]>DivisorSigma[0,#]&] (* Ivan N. Ianakiev, Aug 13 2015 *)

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

use ntheory ":all"; my @A = grep { my $d=scalar(divisors($)); scalar(divisors($+$d)) > $d; } 1..100; say "@A"; # Dana Jacobsen, Apr 28 2017

A348337 For n >= 1; x = n, then iterate x --> x + d(x) until d(x + d(x)) >= d(x). a(n) gives the number of iteration steps where d(i) is the number of divisors of i, A000005(i).

Original entry on oeis.org

3, 2, 7, 1, 6, 5, 5, 4, 4, 4, 3, 3, 2, 3, 1, 1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 2, 2, 1, 2, 3, 1, 2, 3, 1, 3, 3, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 3, 3, 6, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 3, 5, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 4, 1, 2, 5, 4, 5, 1, 4, 4, 1, 4, 3, 3, 3, 3, 2, 1

Offset: 1

Ctibor O. Zizka, Oct 13 2021

nonn

a(n) = 1 for n from A260577.

			n = 1; x(1) = 1 + d(1) = 2, d(1 + d(1)) >= d(1) thus x(2) = 2 + d(2) = 4, d(2 + d(2)) >= d(2) thus x(3) = 4 + d(4) = 7, d(4 + d(4)) < d(4), stop. a(1) = 3.

Cf. A000005, A062249, A175304, A259934, A260577, A286529.

d[n_] := DivisorSigma[0, n]; x[n_] := n + d[n]; a[n_] := Length@ NestWhileList[x, n, d[#] <= d[x[#]] &]; Array[a, 100] (* Amiram Eldar, Oct 15 2021 *)

cp's OEIS Frontend

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

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