A275217 Even numbers n such that A000005(n) divides A000005(n^n).

4, 16, 64, 100, 196, 484, 676, 1024, 1156, 1296, 1444, 1936, 2116, 3364, 3844, 4096, 4900, 5476, 5776, 6400, 6724, 7396, 8836, 10816, 11236, 12100, 13456, 13924, 14884, 15376, 16900, 17956, 20164, 21316, 23716, 24964, 26896, 27556, 28900, 31684, 33124, 36100

Offset

1,1

Comments

This sequence is not the duplicate of A275123. See also comments section of A275123.

An even number n with prime factorization Product_i p_i^(e_i) is in this sequence iff Product_i (n*e_i+1)/(e_i+1) is an integer.

This sequence is infinite since A002110(n)^2 / 9 is always a term of this sequence for n > 1.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

4 is a term because 4 = 2^2 and (4*2+1) mod (2+1) = 0.

Prog

(PARI) is(n, f=factor(n))=f=f[, 2]; n%2==0 && denominator(prod(i=1, #f, (f[i]*n+1)/(f[i]+1)))==1 \\ Charles R Greathouse IV, Jul 20 2016

Crossrefs

Cf. A000005, A062319, A275123.

Sequence in context: A029993 A268066 A275123 * A158988 A337968 A328850

Adjacent sequences: A275214 A275215 A275216 * A275218 A275219 A275220

Keyword

nonn

Author

Altug Alkan, Jul 20 2016

Status

approved