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 A055638 #55 Mar 21 2025 10:01:44
%S A055638 2,3,4,5,8,17,27,41,49,59,64,71,89,101,125,131,167,169,173,256,289,
%T A055638 293,383,512,529,677,701,729,743,761,773,827,839,841,857,911,1091,
%U A055638 1097,1163,1181,1193,1217,1373,1427,1487,1559,1583,1709,1811,1847,1849,1931
%N A055638 Numbers k for which sigma(k^2) is prime.
%C A055638 sigma(n) is the sum of the divisors of n (A000203).
%C A055638 If sigma(x) is prime, then x=2 or x=p^(2m), an even power of a prime, cf. A023194. This sequence lists the values n = p^m such that sigma(n^2) is prime, i.e., sqrt( A023194 \ {2} ). The corresponding primes sigma(n^2)=A062700(n) are 1+p+...+p^(2m) = (p^(2m+1)-1)/(p-1), and any prime of that form (cf. A023195) corresponds to a term p^m is in this sequence. - _M. F. Hasler_, Oct 14 2014
%C A055638 This is a subsequence of A000961, see A248963 for its complement therein. - _M. F. Hasler_, Oct 19 2014
%C A055638 a(n) nearly always has digitsum of the form 2 mod 3. Specifically, 99.8% of the first 33733 entries examined conformed. The first exceptions are 3, 4, 27, 49, 64, 169, 256, 289, 529, 729. The exceptions (examined) appear to be integer powers themselves excepting the initial 3. Similarly, except for the initial 3, all entries of A023195 appear to have digitsum = 1 mod 3. - _Bill McEachen_, Mar 05 2017, Mar 20 2025
%C A055638 Number of terms < 10^k: 5, 13, 36, 137, 735, 4730, 33732, 253393, ..., . _Robert G. Wilson v_, Mar 09 2017
%C A055638 Primes in the sequence are A053182. - _Thomas Ordowski_, Nov 18 2017
%H A055638 Robert G. Wilson v, <a href="/A055638/b055638.txt">Table of n, a(n) for n = 1..10000</a> (first 4730 terms from T. D. Noe)
%F A055638 a(n) = sqrt(A023194(n+1)).
%F A055638 Equal to A000961 \ A248963. - _M. F. Hasler_, Oct 19 2014
%t A055638 Select[Range[2000], PrimeQ[DivisorSigma[1, #^2]] &]
%o A055638 (PARI) for(n=1,9999,isprime(sigma(n^2))&&print1(n",")) \\ _M. F. Hasler_, Oct 18 2014
%o A055638 (Magma) [n: n in [1..2000] | IsPrime(SumOfDivisors(n^2))]; // _Vincenzo Librandi_, Oct 18 2014
%Y A055638 Cf. A023194 (sigma(n) is prime).
%Y A055638 Cf. A023195 (primes of the form sigma(n)), A062700 (in order of appearance).
%Y A055638 Cf. A000961, A248963.
%K A055638 nonn
%O A055638 1,1
%A A055638 _Robert G. Wilson v_, Jun 07 2000
%E A055638 Minor edits by _M. F. Hasler_, Oct 18 2014