A263090 Primes p for which A049820(x) = p has a solution.

2, 3, 5, 11, 17, 23, 29, 31, 41, 47, 53, 59, 61, 71, 73, 83, 89, 97, 101, 107, 127, 137, 139, 149, 151, 157, 173, 179, 181, 191, 197, 199, 211, 223, 227, 233, 239, 263, 269, 277, 281, 283, 311, 317, 331, 337, 347, 349, 367, 373, 389, 409, 419, 421, 431, 433, 443, 449, 457, 461, 467, 521, 523, 541, 547, 557, 569, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643

Offset: 1

Author

Antti Karttunen, Oct 11 2015

Keywords

• nonn

Comments

Primes p that there is at least one such k for which k - d(k) = p, where d(k) is the number of divisors of k (A000005).

Examples

			2 is present, as we have 6 - d(6) = 6 - 4 = 2.
3 is present, as we have 5 - d(5) = 3. The same holds for all lesser twin primes (A001359).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..7955

Crossrefs

Complement among primes: A263091.

Intersection of A000040 and A236562.

Cf. A001359 (a subsequence).

Cf. A000005, A049820, A060990.

Cf. also A263094.

Programs

Mathematica

lim = 10000; s = Select[Sort@ DeleteDuplicates@ Table[n - DivisorSigma[0, n], {n, lim}], PrimeQ]; Take[s, 79] (* Michael De Vlieger, Oct 13 2015 *)

PARI

allocatemem(123456789);
uplim1 = 2162160 + 320; \\ = A002182(41) + A002183(41).
v060990 = vector(uplim1);
for(n=3, uplim1, v060990[n-numdiv(n)]++);
A060990 = n -> if(!n,2,v060990[n]);
n=0; forprime(p=2, 131071, if((A060990(p) > 0), n++; write("b263090.txt", n, " ", p)));

Scheme

;; With Antti Karttunen's IntSeq-library.
(define A263090 (MATCHING-POS 1 1 (lambda (n) (and (= 1 (A010051 n)) (not (zero? (A060990 n)))))))