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 A284288 Numbers n such that the average of the strong divisors of n is an integer. 6
 2, 3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 28, 29, 31, 37, 41, 43, 47, 49, 53, 54, 56, 59, 61, 64, 67, 68, 71, 73, 79, 81, 83, 89, 91, 97, 98, 99, 100, 101, 103, 107, 109, 113, 121, 127, 131, 133, 137, 138, 139, 148, 149, 151, 154, 157, 163, 165, 167, 169, 173, 179, 181, 188, 191, 192, 193, 197, 199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS We say d is a strong divisor of n iff d is a divisor of n and d > 1. Numbers n such that A032741(n) divides A039653(n). All primes and squares of primes are in this sequence. Positions of ones in A296082 and A296084. - Antti Karttunen, Dec 05 2017 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 28 is in the sequence because 28 has 6 divisors {1, 2, 4, 7, 14, 28} therefore 5 strong divisors {2, 4, 7, 14, 28}, 2 + 4 + 7 + 14 + 28 = 55 and 5 divides 55. MAPLE filter:= proc(n) local d, t;   d:= numtheory:-divisors(n) minus {1};   convert(d, `+`) mod nops(d) = 0 end proc: select(filter, [\$2..1000]); # Robert Israel, Mar 27 2017 MATHEMATICA Select[Range[2, 200], Mod[DivisorSigma[1, #1] - 1, DivisorSigma[0, #1] - 1] == 0 &] PROG (PARI) for(n=2, 200, if((sigma(n) - 1)%(numdiv(n) - 1)==0, print1(n, ", "))) \\ Indranil Ghosh, Mar 24 2017 (Python) from sympy.ntheory import divisor_sigma, divisor_count print [n for n in range(2, 201) if (divisor_sigma(n) - 1)%(divisor_count(n) - 1) == 0] # Indranil Ghosh, Mar 24 2017 CROSSREFS Cf. A000203, A000430, A003601, A023884, A023886, A032741, A039653, A296082, A296084 (characteristic function). Sequence in context: A253063 A081998 A325266 * A074583 A001092 A327782 Adjacent sequences:  A284285 A284286 A284287 * A284289 A284290 A284291 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 24 2017 STATUS approved

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Last modified June 5 09:46 EDT 2020. Contains 334829 sequences. (Running on oeis4.)