A307967 -id:A307967 - cp's OEIS frontend

A307982 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).

1, 1, 1, 1, 1, 3, 3, 6, 3, 11, 5, 15, 8, 19, 7, 36, 10, 31, 15, 60, 12, 56, 17, 97, 24, 72, 19, 170, 29, 94, 32, 229, 31, 156, 34, 334, 47, 182, 46, 471, 49, 218, 68, 658, 51, 314, 70, 797, 84, 354, 72, 1173, 93, 437, 98, 1353, 95, 576, 114, 1792, 131, 640, 116, 2243, 133

Offset: 1

Ilya Gutkovskiy, May 11 2019

nonn

Shifts 4 places left when inverse Moebius transform applied twice.

Cf. A000005, A007557, A307967, A307994, A308083, A319133.

a[n_] := a[n] = Sum[DivisorSigma[0, (n - 4)/d] a[d], {d, Divisors[n - 4]}]; a[1] = a[2] = a[3] = a[4] = 1; Table[a[n], {n, 1, 65}]

a(1) = ... = a(4) = 1; a(n+4) = Sum_{d|n} tau(n/d)*a(d), where tau = number of divisors (A000005).

A308083 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 + x^5 * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 3, 3, 6, 3, 9, 5, 12, 11, 11, 11, 22, 14, 23, 19, 29, 24, 41, 25, 40, 41, 48, 43, 66, 45, 71, 67, 86, 68, 95, 73, 113, 110, 118, 107, 157, 115, 162, 148, 182, 159, 225, 164, 235, 229, 247, 227, 296, 244, 328, 297, 357, 298, 413, 352, 452, 409, 436, 415, 575

Offset: 1

Ilya Gutkovskiy, May 11 2019

nonn

Shifts 5 places left when inverse Moebius transform applied twice.

Cf. A000005, A007557, A307967, A307982, A307995, A319133.

a[n_] := a[n] = Sum[DivisorSigma[0, (n - 5)/d] a[d], {d, Divisors[n - 5]}]; a[1] = a[2] = a[3] = a[4] = a[5] = 1; Table[a[n], {n, 1, 65}]

a(1) = ... = a(5) = 1; a(n+5) = Sum_{d|n} tau(n/d)*a(d), where tau = number of divisors (A000005).

cp's OEIS Frontend

A307982 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).

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