A275123 -id:A275123 - cp's OEIS frontend

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

Altug Alkan, Jul 20 2016

nonn

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.

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

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

Cf. A000005, A062319, A275123.

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

A280387 Composite numbers n such that sum of proper divisors of n divides sum of proper divisors of n^n.

Original entry on oeis.org

4, 8, 9, 16, 21, 25, 27, 32, 36, 45, 49, 64, 81, 87, 91, 99, 121, 125, 128, 144, 169, 196, 217, 243, 256, 289, 325, 343, 361, 400, 417, 481, 512, 529, 559, 625, 685, 697, 703, 721, 729, 745, 749, 775, 801, 841, 925, 931, 961, 1024, 1156, 1157, 1261, 1331

Offset: 1

Altug Alkan, Jan 01 2017

Terms are 2^2, 2^3, 3^2, 2^4, 3*7, 5^2, 3^3, 2^5, 2^2*3^2, 3^2*5, 7^2, 2^6, 3^4, 3*29, 7*13, 3^2*11, 11^2, 5^3, ...

Terms that are not Duffinian numbers are 45, 87, 91, 99, 196, 703, 745, 775, 801, 931, ...

			Composite number 21 is a term because (sigma(21) - 21) = 11 divides (sigma(21^21) - 21^21) = 4381940263463668467705506011

Cf. A000203, A001065, A003624, A275123.

Select[Range[10^3], And[CompositeQ@ #, Divisible @@ Map[DivisorSigma[1, #] - # &, {#^#, #}]] &] (* Michael De Vlieger, Jan 02 2017 *)

is(n) = !isprime(n) && (sigma(n^n)-n^n)%(sigma(n)-n)==0;

More terms from Amiram Eldar, Feb 19 2019

cp's OEIS Frontend

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

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