A072344 -id:A072344 - cp's OEIS frontend

A072917 a(n) = p(n) - phi(n), where p(n) is the least prime greater than phi(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 1, 3, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 3, 5, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 5, 5, 3, 1, 5, 3, 5, 1, 5, 1, 1, 1, 1, 1, 5, 1, 5, 5, 1, 1, 5, 3, 1, 3, 1, 1, 5, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1

Offset: 1

Joseph L. Pe, Aug 11 2002

			phi(15) = 8 and the least prime > 8 is 11; hence a(15) = 11 - 8 = 3.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000010, A013632, A072344.

a[n_] := Module[{r, p}, p = EulerPhi[n]; r = p + 1; While[ ! PrimeQ[r], r = r + 1]; r - p]; Table[a[i], {i, 1, 100}]
lpg[n_]:=Module[{ep=EulerPhi[n]},NextPrime[ep]-ep]; Array[lpg,200] (* Harvey P. Dale, May 29 2017 *)

A072917(n) = (nextprime(1+eulerphi(n)) - eulerphi(n)); \\ Antti Karttunen, Aug 22 2017

a(n) = A013632(A000010(n)). - Antti Karttunen, Aug 22 2017

A072341 a(n) = the least natural number k such that k*sigma(n) + 1 is prime.

Original entry on oeis.org

1, 2, 1, 4, 1, 1, 2, 2, 4, 1, 1, 1, 2, 3, 3, 10, 1, 2, 2, 1, 3, 1, 3, 1, 10, 1, 1, 2, 1, 1, 3, 2, 2, 2, 2, 6, 5, 1, 2, 2, 1, 1, 2, 4, 1, 1, 2, 3, 4, 4, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 5, 1, 3, 4, 4, 3, 2, 1, 1, 3, 1, 6, 2, 2, 3, 2, 1, 2, 3, 2, 6, 1, 4, 2, 1, 3, 2, 1, 2, 4, 1, 2, 2, 3, 2, 3, 2, 12, 1, 6, 1, 2, 3

Offset: 1

Joseph L. Pe, Jul 16 2002

nonn

Conjecture: a(n) is less than or equal to n for all n.

			sigma(4) = 7 and the least natural number k such that 7 k + 1 is prime is k = 4; so a(4) = 4.

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A000203, A034693, A034694, A072344.

f[n_] := Module[{i}, i = 0; While[ ! PrimeQ[i*DivisorSigma[1, n] + 1], i++ ]; i]; Table[f[i], {i, 1, 150}]

A072341(n) = { my(k=1,s=sigma(n)); while(!isprime(1+(k*s)),k++); k; }; \\ Antti Karttunen, Nov 07 2017

a(n) = A034693(A000203(n)). - Antti Karttunen, Nov 07 2017

cp's OEIS Frontend

A072917 a(n) = p(n) - phi(n), where p(n) is the least prime greater than phi(n).

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