A358452 The inverse Euler transform of p(n) = n if n is prime, otherwise 1.

1, 1, 1, 1, -3, 3, -3, 5, -8, 5, -11, 36, -45, 41, -72, 142, -223, 311, -493, 851, -1243, 1823, -3204, 5336, -7906, 12083, -20134, 33133, -51685, 81568, -133556, 215363, -340155, 547916, -895895, 1442323, -2300704, 3718260, -6056908, 9787064, -15755664, 25541623

Offset: 0

Author

Peter Luschny, Nov 21 2022

Keywords

• sign

Comments

Conjecture: signum(a(n)) + (-1)^n = 0 for n >= 3.

Links

• N. J. A. Sloane, Transforms.
• Wiki, Euler_transform

Crossrefs

Cf. A089026, A219224.

Programs

Maple

# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(n -> ifelse(isprime(n), n, 1)):
seq(a(n), n = 0..41);
# Using EULERi the sequence is returned without a(0) and has offset 1.
f := n -> ifelse(isprime(n), n, 1): EULERi([seq(f(n), n = 1..41)]);