A383288 Numbers k for which A276075(k) is a multiple of 4, where A276075 is fully additive with a(p) = PrimePi(p)!.

1, 7, 9, 11, 12, 13, 15, 16, 17, 19, 20, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 63, 67, 71, 73, 77, 79, 81, 83, 84, 89, 91, 97, 99, 101, 103, 105, 107, 108, 109, 112, 113, 117, 119, 121, 127, 131, 132, 133, 135, 137, 139, 140, 143, 144, 149, 151, 153, 156, 157, 161, 163, 165, 167, 169, 171, 173, 175, 176

Offset

1,2

Comments

All primes > 5 are included.

A multiplicative semigroup; if m and n are in the sequence then so is m*n. - Antti Karttunen, Jan 20 2026

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to factorial base representation.

Index entries for sequences related to prime indices in the factorization of n.

Example

7 = prime(4), and because 4 divides 24 (= 4!), 7 is present.
9 = prime(2)*prime(2), and because 4 divides 2! + 2! = 4, 9 is present.

Prog

(PARI) isA383288 = A383287;

Crossrefs

Cf. A276075, A383287 (characteristic function).

Cf. also A339746, A369002.

Sequence in context: A393190 A283056 A162308 * A191883 A108815 A262536

Adjacent sequences: A383285 A383286 A383287 * A383289 A383290 A383291

Keyword

nonn,easy

Author

Antti Karttunen, May 15 2025

Status

approved