cp's OEIS Frontend

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

%I A263091 #15 Mar 16 2025 02:38:27
%S A263091 7,13,19,37,43,67,79,103,109,113,131,163,167,193,229,241,251,257,271,
%T A263091 293,307,313,353,359,379,383,397,401,439,463,479,487,491,499,503,509,
%U A263091 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 A263091 Primes p for which A049820(x) = p has no solution.
%C A263091 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 A263091 Antti Karttunen, <a href="/A263091/b263091.txt">Table of n, a(n) for n = 1..15383</a>
%t A263091 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 A263091 (PARI)
%o A263091 allocatemem(123456789);
%o A263091 uplim1 = 2162160 + 320; \\ = A002182(41) + A002183(41).
%o A263091 v060990 = vector(uplim1);
%o A263091 for(n=3, uplim1, v060990[n-numdiv(n)]++);
%o A263091 A060990 = n -> if(!n,2,v060990[n]);
%o A263091 n=0; forprime(p=2, 524287, if((0 == A060990(p)), n++; write("b263091.txt", n, " ", p)));
%o A263091 (Scheme)
%o A263091 ;; With _Antti Karttunen_'s IntSeq-library.
%o A263091 (define A263091 (MATCHING-POS 1 1 (lambda (n) (and (= 1 (A010051 n)) (zero? (A060990 n))))))
%Y A263091 Complement among primes: A263090.
%Y A263091 Intersection of A000040 and A045765.
%Y A263091 Subsequence of A067774 (A049591).
%Y A263091 Cf. A000005, A049820, A060990.
%K A263091 nonn
%O A263091 1,1
%A A263091 _Antti Karttunen_, Oct 11 2015