A359213 -id:A359213 - cp's OEIS frontend

A097379 Numbers m such that 1+SquareFreeKernel(m) is prime.

1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 30, 32, 36, 40, 42, 44, 46, 48, 50, 54, 58, 60, 64, 66, 70, 72, 78, 80, 82, 84, 88, 90, 92, 96, 100, 102, 106, 108, 116, 120, 126, 128, 130, 132, 138, 140, 144, 150, 156, 160, 162, 164, 166, 168, 176, 178, 180, 184, 190, 192

Offset: 1

Reinhard Zumkeller, Aug 11 2004

nonn

			m = 100 = (2*5)^2 -> A076618(100) = 1+2*5 = 11 = A000040(5), therefore 100 is a term.

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

Cf. A007947, A076618, A039787, A097380, A097381, A359213.

Select[Range[200], PrimeQ[1 + Times @@ FactorInteger[#][[;; , 1]]] &] (* Amiram Eldar, Feb 01 2024 *)

is(n) = isprime(1 + vecprod(factor(n)[, 1])); \\ Amiram Eldar, Feb 01 2024

A076618(a(n)) = A007947(a(n))+1 is prime.

A374593 Numbers k such that k - rad(k) + 1 is prime, where rad(k) is the radical A007947(k).

Original entry on oeis.org

4, 8, 9, 12, 18, 20, 24, 32, 36, 40, 44, 45, 48, 49, 50, 56, 60, 63, 72, 75, 80, 81, 84, 88, 90, 92, 99, 104, 108, 116, 117, 128, 132, 136, 140, 144, 147, 153, 156, 160, 162, 164, 168, 169, 180, 184, 200, 204, 207, 212, 216, 224, 225, 234, 240, 243, 245, 250

Offset: 1

Arsen Vardanyan, Aug 23 2024

nonn

Includes 4*p for p in A005384, 8*p for p in A007693, and 16*p for p in A228857. - Robert Israel, Jun 27 2025

			12 is a term, because 12 - rad(12) + 1 = 12 - (2*3) + 1 = 12 - 6 + 1 = 7 is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A005384, A007693, A007947, A097379, A228857, A359213.

rad:= n -> convert(numtheory:-factorset(n),`*`):
select(k -> isprime(k - rad(k)+1), [$1..1000]); # Robert Israel, Jun 27 2025

rad[n_] := Times @@ (First@# & /@ FactorInteger@ n);Select[Range[250],PrimeQ[#-rad[#]+1]&] (* James C. McMahon, Sep 27 2024 *)

isok(k) = isprime(k - (factorback(factor(k)[, 1])) + 1);

A375777 Numbers k such that k - rad(k) - 1 is prime, where rad(k) is A007947(k).

Original entry on oeis.org

8, 9, 12, 16, 18, 24, 25, 27, 28, 32, 36, 40, 45, 48, 49, 54, 56, 60, 63, 64, 75, 76, 84, 90, 96, 98, 100, 108, 112, 120, 121, 124, 126, 136, 144, 148, 152, 153, 160, 171, 175, 180, 184, 189, 196, 198, 204, 207, 208, 220, 228, 232, 243, 250, 261, 264, 270, 276

Offset: 1

Arsen Vardanyan, Aug 27 2024

nonn

			12 is a term, because 12 - rad(12) - 1 = 12 - (2 * 3) - 1 = 12 - 6 - 1 = 5 is prime.

Cf. A007947, A097379, A359213, A374593.

Select[Range[300], PrimeQ[# - Times @@ FactorInteger[#][[;; , 1]] - 1] &] (* Amiram Eldar, Aug 27 2024 *)

isok(k) = isprime(k - (vecprod(factor(k)[, 1])) - 1);

cp's OEIS Frontend

A097379 Numbers m such that 1+SquareFreeKernel(m) is prime.

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A374593 Numbers k such that k - rad(k) + 1 is prime, where rad(k) is the radical A007947(k).

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A375777 Numbers k such that k - rad(k) - 1 is prime, where rad(k) is A007947(k).

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Mathematica

PARI