A277994 -id:A277994 - cp's OEIS frontend

A274915 Powers of odd non-Fermat primes.

1, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset: 1

Juri-Stepan Gerasimov, Nov 11 2016

n is in the sequence if n = p^m where p is in A138889 and m >= 0. - Robert Israel, Sep 15 2017
The difference between two divisors of n is never a power of 2. The first number with this property that is not in the sequence is 91. - Robert Israel, Sep 15 2017
Subsequence of A061345.

			49 is in this sequence because 49 = 7^2 and 7 is not a Fermat prime.

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

Cf. A019434, A061345, A092506, A138889, A277994.

N:= 500: # to get all terms <= N
P:= select(isprime, {seq(i,i=7..N,2)}) minus {seq(2^i+1, i=1..ilog2(N))}:
sort(convert(map(p -> seq(p^k,k=0..floor(log[p](N))), P), list)); # Robert Israel, Sep 15 2017

A277994(a(n)) = 0.

Edited, new name, and corrected by Robert Israel, Sep 15 2017

A272608 Number of positive integers k such that both n/(k + 2^x) and n/(n/k - 2^y) are integers for some nonnegative x, y.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 0, 3, 1, 2, 0, 4, 0, 0, 1, 4, 1, 2, 0, 3, 1, 0, 0, 6, 0, 0, 0, 0, 0, 3, 0, 5, 2, 2, 1, 4, 0, 0, 0, 4, 0, 2, 0, 0, 1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 5, 0, 0, 1, 6, 2, 4, 0, 2, 0, 1, 0, 6, 0, 0, 0, 0, 1, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2

Offset: 1

Juri-Stepan Gerasimov, Nov 09 2016

nonn

Where k, k + 2^x, n/k, n/k - 2^y, n/(k + 2^x) and n/(n/k - 2^y) are divisors of n.

			a(9) = 1 because both 9/(1 + 2^1) = 3 and 9/(9/1 - 2^4) = 1 are integers.
a(68) = 3 because (1) 68/(1 + 2^0) = 34 and 68/(68 - 2^6) = 17, (2) 68/(2 + 2^1) = 17 and 68/(34 - 2^5) = 34, and (3) 68/(4 + 2^6) = 1 and 68/(17 - 2^4) = 68 are all integers.

Cf. A027750, A092506, A277994.

t1(n,k)=for(x=0,logint(n,2), if(n%(k+2^x)==0, return(1))); 0
t2(n,d)=for(y=0,logint(d-1,2), if(n%(d-2^y)==0, return(1))); 0
a(n)=sumdiv(n,k, kCharles R Greathouse IV, Nov 09 2016

a(2^n) = n, a(A092506(n)) = 1.

a(68), a(70), a(90) corrected by Charles R Greathouse IV, Nov 09 2016

cp's OEIS Frontend

A274915 Powers of odd non-Fermat primes.

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