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).

5808, 9911, 34317, 113147, 750735, 1600573, 5546909, 9380741, 23316851, 71271069, 98488755, 233043067, 384847485, 485930975, 751588475, 1356370173, 2299880351, 2710679045, 4306310927, 5734323819, 6578172579, 9721485395, 12413061671, 17537591045, 26866372821

Offset

1,1

Comments

When p>=7, this is the number of isomorphism classes of groups of order p^7. See p. 2 of the Misseldine link.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015 (Table 1.1, 7th row.)

Maple

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

Mathematica

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}]

Prog

(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)];

Crossrefs

Cf. A269748, A269749.

Sequence in context: A233045 A031618 A206655 * A251920 A348821 A104284

Adjacent sequences: A270863 A270864 A270865 * A270867 A270868 A270869

Keyword

nonn

Author

Vincenzo Librandi, Apr 01 2016

Status

approved