A063015 -id:A063015 - cp's OEIS frontend

A063452 Numbers k such that k - mu(k) is prime.

2, 6, 14, 30, 38, 42, 62, 66, 70, 74, 78, 102, 130, 138, 158, 190, 194, 222, 238, 278, 282, 310, 314, 366, 390, 398, 418, 422, 430, 438, 442, 458, 462, 498, 510, 542, 570, 598, 606, 614, 618, 642, 646, 658, 662, 674, 682, 734, 742, 758, 770, 786, 798, 822

Offset: 1

Jason Earls, Jul 25 2001

nonn

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A063015, A062304.

[n: n in [1..1000] |IsPrime(n - MoebiusMu(n))]; // Vincenzo Librandi, Jun 26 2018

Select[Range[1, 1000], PrimeQ[# - MoebiusMu[#]] &] (* Vincenzo Librandi, Jun 26 2018 *)

PARI
```
ok(m)={isprime(m - moebius(m))}
```

A076369 a(n) = n + mu(n), where mu is the Moebius function (A008683).

Original entry on oeis.org

2, 1, 2, 4, 4, 7, 6, 8, 9, 11, 10, 12, 12, 15, 16, 16, 16, 18, 18, 20, 22, 23, 22, 24, 25, 27, 27, 28, 28, 29, 30, 32, 34, 35, 36, 36, 36, 39, 40, 40, 40, 41, 42, 44, 45, 47, 46, 48, 49, 50, 52, 52, 52, 54, 56, 56, 58, 59, 58, 60, 60, 63, 63, 64, 66, 65, 66, 68, 70, 69, 70, 72

Offset: 1

Reinhard Zumkeller and Labos Elemer, Oct 14 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000027, A005117, A008683, A013929, A063015, A076840.

a[n_] := n + MoebiusMu[n]; Array[a, 100] (* Amiram Eldar, Apr 09 2025 *)

a(n) = n + moebius(n); \\ Amiram Eldar, Apr 09 2025

a(n) = n + mu(m) = A000027(n) + A008683(n).

a(n) = n iff n is not squarefree: a(A013929(k)) = A013929(k) and a(A005117(k)) <> A005117(k).

A075431 Primes of the form n+mu(n), where mu is the Moebius function (A008683).

Original entry on oeis.org

2, 7, 11, 23, 29, 41, 47, 59, 83, 101, 107, 109, 113, 137, 167, 173, 179, 181, 211, 227, 229, 257, 263, 281, 317, 331, 347, 353, 359, 373, 383, 401, 409, 433, 463, 467, 479, 503, 547, 563, 571, 587, 601, 617, 641, 653, 677, 691, 709, 719, 761, 821, 829, 839, 853

Offset: 1

Reinhard Zumkeller, Sep 15 2002

nonn

Subsequence of A075430.

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Cf. A063015, A039787, A049097.

isok(p)={isprime(p) && (moebius(p+1) == -1 || moebius(p-1) == 1)} \\ Andrew Howroyd, Apr 20 2021

Terms a(41) and beyond from Andrew Howroyd, Apr 20 2021

cp's OEIS Frontend

A063452 Numbers k such that k - mu(k) is prime.

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A076369 a(n) = n + mu(n), where mu is the Moebius function (A008683).

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A075431 Primes of the form n+mu(n), where mu is the Moebius function (A008683).

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