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A263091
Primes p for which A049820(x) = p has no solution.
5
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
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).
Sequence in context: A029710 A145897 A078863 * A320533 A059351 A320532
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 11 2015
STATUS
approved