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 A183100 a(n) = sum of divisors d of n which are either 1 or of the form Product_(i) (p_i^e_i) where the e_i are <= 1. 4

%I

%S 1,3,4,3,6,12,8,3,4,18,12,24,14,24,24,3,18,30,20,38,32,36,24,48,6,42,

%T 4,52,30,72,32,3,48,54,48,42,38,60,56,78,42,96,44,80,69,72,48,96,8,68,

%U 72,94,54,84,72,108,80,90,60,164,62,96,95,3,84,144,68,122,96,144,72,66,74,114,99,136,96,168,80,158,4,126,84,220,108,132,120,168,90,225,112,164,128,144,120,192,98,122,147,88

%N a(n) = sum of divisors d of n which are either 1 or of the form Product_(i) (p_i^e_i) where the e_i are <= 1.

%C a(n) = sum of non-powerful divisors d of n where powerful numbers are numbers from A001694(m) for m >=1.

%H Antti Karttunen, <a href="/A183100/b183100.txt">Table of n, a(n) for n = 1..16385</a>

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>

%F a(n) = A000203(n) - A183099(n) = A183098(n) + 1.

%F a(1) = 1, a(p) = p+1, a(pq) = (p+1)*(q+1), a(pq...z) = (p+1)*(q+1)*…*(z+1), a(p^k) = p+1, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.

%e For n = 12, set of such divisors is {1, 2, 3, 6, 12}; a(12) = 1+2+3+6+12 = 24.

%o (PARI) A183100(n) = (1 + sumdiv(n, d, d*(!ispowerful(d)))); \\ _Antti Karttunen_, Oct 07 2017

%Y Cf. A000203, A001694, A183098, A183099.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Dec 25 2010

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)