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 A065302 #19 Jun 05 2025 00:43:18 %S A065302 1,26,74,122,146,218,314,362,386,458,554,626,746,794,818,842,866,914, %T A065302 1082,1202,1226,1322,1346,1418,1466,1514,1538,1658,1706,1754,1874, %U A065302 1994,2018,2042,2066,2138,2186,2234,2258,2306,2402,2426,2474,2594,2642,2762 %N A065302 Squarefree nonprime numbers whose sum of divisors is also squarefree. %C A065302 All elements except the first, a(1)=1, are of the form 2*p, where p is a prime and p == 1 (mod 12). Also, sigma(2*p) = (1+2)*(1+p) = 6m where m = (1+p)/2 and m == 1 (mod 6). A squarefree composite number not of the form 2*p cannot be in the sequence since sigma is multiplicative. For example, sigma(p*q) = (1+p)*(1+q) is divisible by 4 for p,q > 2. - _Walter Kehowski_, Mar 21 2007 %H A065302 Harry J. Smith, <a href="/A065302/b065302.txt">Table of n, a(n) for n = 1..1000</a> %t A065302 Select[Range[3000], !PrimeQ[#] && SquareFreeQ[#] && SquareFreeQ[DivisorSigma[1, #]] &] (* _Amiram Eldar_, Jun 05 2025 *) %o A065302 (PARI) isok(m) = !isprime(m) && moebius(m) && moebius(sigma(m)); \\ _Harry J. Smith_, Oct 16 2009 %Y A065302 Cf. A000203, A008683, A065299, A065300, A065301, A065303. %Y A065302 Cf. A128607, A128608. %K A065302 nonn %O A065302 1,2 %A A065302 _Labos Elemer_, Oct 29 2001 %E A065302 Name corrected by _Amiram Eldar_, Jun 05 2025