This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347038 #37 Aug 07 2025 03:01:28 %S A347038 29,37,41,53,67,89,101,109,113,127,137,151,157,173,181,197,227,229, %T A347038 233,257,269,277,281,293,313,349,373,389,401,409,421,439,461,557,587, %U A347038 593,601,613,617,641,643,653,661,673,677,701,709,739,761,773,787,821,829 %N A347038 Primes p such that there are no solutions to d(k+p) = sigma(k). %C A347038 If p is not in the sequence and d(k+p) = sigma(k), then k <= 1+2*sqrt(p). Proof: We have d(m) <= 2*sqrt(m) (see formula in A000005), so 2*sqrt(k+p) >= d(k+p) = sigma(k) >= k+1 (if k > 1). After squaring and simplifying, we get k <= 1+2*sqrt(p). - _Pontus von Brömssen_, Aug 20 2021 %H A347038 Robert Israel, <a href="/A347038/b347038.txt">Table of n, a(n) for n = 1..10000</a> %p A347038 filter:= proc(p) isprime(p) and not ormap(k -> numtheory:-tau(k+p) = numtheory:-sigma(k), [$1 .. 1 + 2*isqrt(p)]) end proc: %p A347038 select(filter, [seq(i,i=3..1000,2)]); # _Robert Israel_, Aug 06 2025 %o A347038 (Python) %o A347038 from sympy import divisor_count as d, divisor_sigma as sigma, primerange %o A347038 from math import isqrt %o A347038 def A347038_list(pmax): %o A347038 a = [] %o A347038 for p in primerange(2, pmax + 1): %o A347038 if not any(d(k + p) == sigma(k) for k in range(1, 2 + isqrt(4 * p))): %o A347038 a.append(p) %o A347038 return a # _Pontus von Brömssen_, Aug 20 2021 %Y A347038 Cf. A000005, A000203, A247485. %K A347038 nonn %O A347038 1,1 %A A347038 _Angad Singh_, Aug 12 2021