A191558 -id:A191558 - cp's OEIS frontend

A101203 a(n) = sum of nonprimes <= n.

0, 1, 1, 1, 5, 5, 11, 11, 19, 28, 38, 38, 50, 50, 64, 79, 95, 95, 113, 113, 133, 154, 176, 176, 200, 225, 251, 278, 306, 306, 336, 336, 368, 401, 435, 470, 506, 506, 544, 583, 623, 623, 665, 665, 709, 754, 800, 800, 848, 897, 947, 998, 1050, 1050, 1104, 1159, 1215

Offset: 0

Reinhard Zumkeller, Jan 23 2005

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A062298, A018252.
Partial sums of A191558.
Cf. A000217, A034387, A101256.

a101203 n = a101203_list !! (n-1)
a101203_list = scanl (+) 0 $ zipWith (*) [1..] $ map (1 -) a010051_list
-- Reinhard Zumkeller, Oct 10 2013

Accumulate[Table[If[PrimeQ[n],0,n],{n,0,60}]] (* Harvey P. Dale, Oct 02 2020 *)

my(s=0); for(k=0,100,if(!isprime(k),s+=k);print1(s", ")); \\ Cino Hilliard, Feb 04 2006

a(n) = A000217(n) - A034387(n) = A101256(n) + 1.

A125071 a(n) = sum of the exponents in the prime factorization of n which are not primes.

Original entry on oeis.org

0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 1, 1, 3, 1, 0, 2, 2, 2, 0, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 5, 0, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 6, 2, 3, 1, 1, 2, 3, 1, 0, 1, 2, 1, 1, 2, 3, 1, 5, 4, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 3, 1, 1, 3

Offset: 1

Leroy Quet, Nov 18 2006

			720 has the prime-factorization of 2^4 *3^2 *5^1. Two of these exponents, 4 and 1, aren't primes. So a(720) = 4 + 1 = 5.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from exponents in factorization of n.

Cf. A001222, A077761, A191558, A125070.

f[n_] := Plus @@ Select[Last /@ FactorInteger[n], ! PrimeQ[ # ] &];Table[f[n], {n, 110}] (* Ray Chandler, Nov 19 2006 *)

A125071(n) = vecsum(apply(e -> if(isprime(e),0,e), factorint(n)[, 2])); \\ Antti Karttunen, Jul 07 2017

From Amiram Eldar, Sep 30 2023: (Start)
Additive with a(p^e) = A191558(e).
Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B - C), where B is Mertens's constant (A077761) and C = Sum_{p prime} p * (P(p) - P(p+1)) - Sum_{k>=2} P(k) = 0.20171354082810650948..., where P(s) is the prime zeta function. (End)

Extended by Ray Chandler, Nov 19 2006

A259175 a(n) = 1 if n prime, otherwise prime(n).

Original entry on oeis.org

2, 1, 1, 7, 1, 13, 1, 19, 23, 29, 1, 37, 1, 43, 47, 53, 1, 61, 1, 71, 73, 79, 1, 89, 97, 101, 103, 107, 1, 113, 1, 131, 137, 139, 149, 151, 1, 163, 167, 173, 1, 181, 1, 193, 197, 199, 1, 223, 227, 229, 233, 239, 1, 251, 257, 263, 269, 271, 1, 281, 1, 293, 307, 311

Offset: 1

Vincenzo Librandi, Jun 20 2015

The subsequence of prime terms is A007821. - Michel Marcus, Jun 20 2015

			a(7) = 1 because 7 is prime.
a(8) = 19 because 8 is not prime and prime(8) = 19.

Cf. A007821, A010051, A061397, A191558.

[IsPrime(n) select 1 else NthPrime(n): n in [1..100]];

Table[If[PrimeQ[n], 1, Prime[n]], {n, 100}]

A272476 a(n) = n if n is prime, a(n) = 2*n+3 otherwise.

Original entry on oeis.org

3, 5, 2, 3, 11, 5, 15, 7, 19, 21, 23, 11, 27, 13, 31, 33, 35, 17, 39, 19, 43, 45, 47, 23, 51, 53, 55, 57, 59, 29, 63, 31, 67, 69, 71, 73, 75, 37, 79, 81, 83, 41, 87, 43, 91, 93, 95, 47, 99, 101, 103, 105, 107, 53, 111, 113, 115, 117, 119, 59, 123, 61, 127

Offset: 0

Vincenzo Librandi, May 02 2016

Prime numbers repeated: 3, 5, 11, 19, 23, 31, 43, 47, 53, 59, 67, 71, ..., that is A065091 without A089531.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A000040, A018252.

Cf. A061397, A191558.

[IsPrime(n) select n else 2*n+3: n in [0..80]];

Table[If[PrimeQ[n], n, 2 n + 3], {n, 0, 150}]

A259182 a(n) = prime(n) if n prime otherwise 1.

Original entry on oeis.org

1, 3, 5, 1, 11, 1, 17, 1, 1, 1, 31, 1, 41, 1, 1, 1, 59, 1, 67, 1, 1, 1, 83, 1, 1, 1, 1, 1, 109, 1, 127, 1, 1, 1, 1, 1, 157, 1, 1, 1, 179, 1, 191, 1, 1, 1, 211, 1, 1, 1, 1, 1, 241, 1, 1, 1, 1, 1, 277, 1, 283, 1, 1, 1, 1, 1, 331, 1, 1, 1, 353, 1, 367, 1, 1, 1, 1

Offset: 1

Vincenzo Librandi, Jun 20 2015

The subsequence of prime terms is A006450.

			a(7) = 17 because prime(7) = 17 is prime.
a(8) = 1 because 8 is not prime.

Cf. A006450, A007821, A010051, A061397, A191558, A259175.

[IsPrime(n) select NthPrime(n) else 1: n in [1..100]];

Table[If[! PrimeQ[n], 1, Prime[n]], {n, 100}]

cp's OEIS Frontend

A101203 a(n) = sum of nonprimes <= n.

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A125071 a(n) = sum of the exponents in the prime factorization of n which are not primes.

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A259175 a(n) = 1 if n prime, otherwise prime(n).

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A272476 a(n) = n if n is prime, a(n) = 2*n+3 otherwise.

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Magma

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A259182 a(n) = prime(n) if n prime otherwise 1.

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