A261023 Least number k such that prime(n) = sigma(k) - k - 1.

4, 9, 6, 10, 121, 22, 289, 34, 529, 841, 58, 1369, 30, 82, 2209, 42, 3481, 118, 4489, 5041, 70, 6241, 6889, 78, 9409, 10201, 202, 60, 214, 102, 16129, 17161, 18769, 84, 138, 298, 24649, 26569, 27889, 29929, 32041, 358, 36481, 238, 186, 394, 44521, 49729, 51529

Offset: 1

Author

Paolo P. Lava, Aug 07 2015

Keywords

• nonn
• easy

Comments

For any prime k <= p^2. In fact if k = p^2 we have that sigma(p) = sigma(p^2) - p^2, that is 1 + p = 1 + p + p^2 - p^2.

Examples

			sigma(2) = 3 and 4 is the least number such that sigma(4) - 4 = 7 - 4 = 3.
sigma(13) = 14 and 22 is the least number such that sigma(22) - 22 = 36 - 22 = 14.
		

Links

• Robert Israel and Paolo P. Lava, Table of n, a(n) for n = 1..1229 (first 100 from Paolo P. Lava)

Crossrefs

Cf. A008864, A048050, A070015, A158913.

Programs

Maple

with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do
if isprime(n) then for k from 1 to q do
if sigma(n)=sigma(k)-k then print(k); break; fi; od;
fi; od; end: P(10^9);

Mathematica

Table[k = 1; While[DivisorSigma[1, Prime@ p] != DivisorSigma[1, k] - k, k++]; k, {p, 60}] (* Michael De Vlieger, Aug 07 2015 *)

PARI

a(n) = my(k = 1, p = prime(n)); while(sigma(k)-k-1 != p, k++); k; \\ Michel Marcus, Aug 12 2015

PARI

first(m)=my(v=vector(m),k);for(i=1,m,k=1;while(!(prime(i)==sigma(k)-k-1),k++);v[i]=k;);v; \\ Anders Hellström, Aug 14 2015

Formula

a(n) = A070015(A008864(n)). - Robert Israel, Aug 14 2015