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%I #11 Oct 24 2015 12:31:08
%S 7,13,19,37,43,67,79,103,109,113,131,163,167,193,229,241,251,257,271,
%T 293,307,313,353,359,379,383,397,401,439,463,479,487,491,499,503,509,
%U 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
%N Primes p for which A049820(x) = p has no solution.
%C 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).
%H Antti Karttunen, <a href="/A263091/b263091.txt">Table of n, a(n) for n = 1..15383</a>
%t 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 *)
%o (PARI)
%o allocatemem(123456789);
%o uplim1 = 2162160 + 320; \\ = A002182(41) + A002183(41).
%o v060990 = vector(uplim1);
%o for(n=3, uplim1, v060990[n-numdiv(n)]++);
%o A060990 = n -> if(!n,2,v060990[n]);
%o n=0; forprime(p=2, 524287, if((0 == A060990(p)), n++; write("b263091.txt", n, " ", p)));
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A263091 (MATCHING-POS 1 1 (lambda (n) (and (= 1 (A010051 n)) (zero? (A060990 n))))))
%Y Complement among primes: A263090.
%Y Intersection of A000040 and A045765.
%Y Subsequence of A067774 (A049591).
%Y Cf. A000005, A049820, A060990.
%K nonn
%O 1,1
%A _Antti Karttunen_, Oct 11 2015
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