A263091 Primes p for which A049820(x) = p has no solution.

7, 13, 19, 37, 43, 67, 79, 103, 109, 113, 131, 163, 167, 193, 229, 241, 251, 257, 271, 293, 307, 313, 353, 359, 379, 383, 397, 401, 439, 463, 479, 487, 491, 499, 503, 509, 563, 571, 647, 653, 661, 673, 701, 739, 743, 757, 761, 773, 823, 859, 863, 883, 887, 911, 937, 941, 953, 967, 971, 977, 983, 1009, 1093, 1103, 1109, 1171, 1181, 1193, 1217, 1279, 1283, 1291, 1297, 1307, 1321, 1361

Offset

1,1

Comments

Primes p that there is no such k for which k - d(k) = p, where d(k) is the number of divisors of k (A000005).

Links

Antti Karttunen, Table of n, a(n) for n = 1..15383

Mathematica

lim = 10000; s = Select[Complement[Range@ lim, Sort@ DeleteDuplicates@ Table[n - DivisorSigma[0, n], {n, lim}]], PrimeQ]; Take[s, 76] (* Michael De Vlieger, Oct 13 2015 *)

Prog

(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, 524287, if((0 == A060990(p)), n++; write("b263091.txt", n, " ", p)));
(Scheme, with Antti Karttunen's IntSeq-library)
(define A263091 (MATCHING-POS 1 1 (lambda (n) (and (= 1 (A010051 n)) (zero? (A060990 n))))))

Crossrefs

Complement among primes: A263090.

Intersection of A000040 and A045765.

Subsequence of A067774 (A049591).

Cf. A000005, A049820, A060990.

Sequence in context: A029710 A145897 A078863 * A320533 A059351 A320532

Adjacent sequences: A263088 A263089 A263090 * A263092 A263093 A263094

Keyword

nonn

Author

Antti Karttunen, Oct 11 2015

Status

approved