cp's OEIS Frontend

A270866 a(n) = 3*p^5+12*p^4+44*p^3+170*p^2+707*p+2455 +(4*p^2+44*p+291)*gcd(p-1,3) +(p^2+19*p+135)*gcd(p-1,4) +(3*p+31)*gcd(p-1,5) +4*gcd(p-1,7) +5*gcd(p-1,8) +gcd(p-1,9), where p = prime(n).

%I A270866 #16 Sep 08 2022 08:46:16
%S A270866 5808,9911,34317,113147,750735,1600573,5546909,9380741,23316851,
%T A270866 71271069,98488755,233043067,384847485,485930975,751588475,1356370173,
%U A270866 2299880351,2710679045,4306310927,5734323819,6578172579,9721485395,12413061671,17537591045,26866372821
%N A270866 a(n) = 3*p^5+12*p^4+44*p^3+170*p^2+707*p+2455 +(4*p^2+44*p+291)*gcd(p-1,3) +(p^2+19*p+135)*gcd(p-1,4) +(3*p+31)*gcd(p-1,5) +4*gcd(p-1,7) +5*gcd(p-1,8) +gcd(p-1,9), where p = prime(n).
%C A270866 When p>=7, this is the number of isomorphism classes of groups of order p^7. See p. 2 of the Misseldine link.
%H A270866 Vincenzo Librandi, <a href="/A270866/b270866.txt">Table of n, a(n) for n = 1..1000</a>
%H A270866 Andrew Misseldine, <a href="http://arxiv.org/abs/1508.03757">Counting Schur Rings over Cyclic Groups</a>, arXiv preprint arXiv:1508.03757 [math.RA], 2015 (Table 1.1, 7th row.)
%p A270866 p:=n->ithprime(n): A270866:=n->3*p(n)^5+12*p(n)^4+44*p(n)^3+170*p(n)^2+707*p(n)+2455 +(4*p(n)^2+44*p(n)+291)*gcd(p(n)-1,3) +(p(n)^2+19*p(n)+135)*gcd(p(n)-1,4) +(3*p(n)+31)*gcd(p(n)-1,5) +4*gcd(p(n)-1,7) +5*gcd(p(n)-1,8) +gcd(p(n)-1,9): seq(A270866(n), n=1..35); # _Wesley Ivan Hurt_, Apr 02 2016
%t A270866 Table[3 Prime[n]^5 + 12 Prime[n]^4 + 44 Prime[n]^3 + 170 Prime[n]^2 + 707 Prime[n] + 2455 + (4 Prime[n]^2 + 44 Prime[n] + 291) GCD[Prime[n] - 1, 3] + (Prime[n]^2 + 19 Prime[n]+ 135) GCD[Prime[n] - 1, 4] + (3 Prime[n] + 31) GCD[Prime[n] - 1, 5] + 4 GCD[Prime[n] - 1, 7] + 5 GCD[Prime[n] - 1, 8] + GCD[Prime[n] - 1, 9], {n, 30}]
%o A270866 (Magma) [3*p^5+12*p^4+44*p^3+170*p^2+707*p+2455+(4*p^2+44*p+291)*Gcd(p-1, 3)+(p^2+19*p+135)*Gcd(p-1, 4)+(3*p+31)*Gcd(p-1, 5)+4*Gcd(p-1, 7)+5*Gcd(p-1, 8)+Gcd(p-1, 9): p in PrimesUpTo(200)];
%Y A270866 Cf. A269748, A269749.
%K A270866 nonn
%O A270866 1,1
%A A270866 _Vincenzo Librandi_, Apr 01 2016