0,3

See also: A000217 Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n. A074285 Sum of the divisors of n-th triangular number. A083675 Triangular number for which the sum of the proper divisors is also a triangular number. A000203 sigma(n) = sum of divisors of n. Also called sigma_1(n). A000326 Pentagonal numbers: n(3n-1)/2. A000203 sigma(n) = sum of divisors of n. Also called sigma_1(n). A074285 Sum of the divisors of n-th triangular number. A117948 Sum of the divisors of pentagonal numbers.

n such that A117948(n) is in A000290. n such that SUM[d|A000326(n)] d is in A000290. n such that A000203(A000326(n)) is in A000290. n such that SUM[d|(n*(3*n-1)/2)] d = k^2 for integer k.

a(1) = 1 because sigma[1*(3*1-1)/2)] = 1 = 1^2.

a(2) = 4 because sigma[4*(3*4-1)/2)] = 36 = 6^2.

a(3) = 7 because sigma[7*(3*7-1)/2)] = 144 = 12^2.

a(4) = 12 because sigma[12*(3*12-1)/2)] = 576 = 24^2.

a(5) = 21 because sigma[21*(3*21-1)/2)] = 1024 = 32^2.

a(6) = 23 because sigma[23*(3*23-1)/2)] = 1296 = 36^2.

a(7) = 27 because sigma[27*(3*27-1)/2)] = 3600 = 60^2.

a(8) = 31 because sigma[31*(3*31-1)/2)] = 2304 = 48^2.

a(9) = 71 because sigma[71*(3*71-1)/2)] = 11664 = 108^2.

with(numtheory): a:=proc(n) if type(sqrt(sigma(n*(3*n-1)/2)), integer)=true then n else fi end: seq(a(n), n=0..2200); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2006

Cf. A000203, A000217, A000290, A000326, A074285, A083675, A117948.

Sequence in context: A117950 A022809 A020732 this_sequence A010901 A023624 A123194

Adjacent sequences: A117946 A117947 A117948 this_sequence A117950 A117951 A117952

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 04 2006

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2006