A263091 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.