A071188 -id:A071188 - cp's OEIS frontend

A078545 Duplicate of A071188.

2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 5, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 5, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 7, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 5, 5, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 3

Offset: 2

dead

A071190 Greatest prime factor of sum of divisors of n, for n >= 2; a(1) = 1.

Original entry on oeis.org

1, 3, 2, 7, 3, 3, 2, 5, 13, 3, 3, 7, 7, 3, 3, 31, 3, 13, 5, 7, 2, 3, 3, 5, 31, 7, 5, 7, 5, 3, 2, 7, 3, 3, 3, 13, 19, 5, 7, 5, 7, 3, 11, 7, 13, 3, 3, 31, 19, 31, 3, 7, 3, 5, 3, 5, 5, 5, 5, 7, 31, 3, 13, 127, 7, 3, 17, 7, 3, 3, 3, 13, 37, 19, 31, 7, 3, 7, 5, 31

Offset: 1

Reinhard Zumkeller, May 15 2002

nonn

a(n) is the greatest noncomposite factor of the sum of divisors of n. (Cf. A008578.) - Omar E. Pol, Feb 11 2018

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000203, A006530, A071188, A071189.

Table[FactorInteger[DivisorSigma[1,n]][[-1,1]],{n,80}] (* Harvey P. Dale, Nov 18 2014 *)

a(n) = if (n==1, 1, my(f = factor(sigma(n))); f[#f~,1]); \\ Michel Marcus, Sep 21 2014

a(n) = A006530(A000203(n)).

Name clarified by David A. Corneth and Omar E. Pol, Feb 11 2018

A071187 Smallest prime factor of number of divisors of n; a(1) = 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2

Offset: 1

Reinhard Zumkeller, May 15 2002

a(n) = 2 for nonsquare n. - David A. Corneth, Jul 24 2017

			324 = 18^2 = 2^2 * 3^4 has (2+1)*(4+1) = 3 * 5 = 15 divisors, thus a(324) = A020639(15) = 3. - _Antti Karttunen_, Nov 18 2019

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences computed from exponents in factorization of n.

Cf. A000005, A020639, A071188, A071189, A108951.

Differs from A329614 for the first time at n=324, where a(324) = 3, while A329614(324) = 5. A329613 gives the positions of differences.

a[n_] := FactorInteger[DivisorSigma[0, n]][[1, 1]]; Array[a, 90] (* Jean-François Alcover, Oct 01 2016 *)

A071187(n) = if(1==n, n, my(f = factor(numdiv(n))); vecmin(f[, 1])); \\ Antti Karttunen, Jul 24 2017

first(n) = my(v = vector(n, i, 2)); for(i=1,sqrtint(n), v[i^2] = numdiv(i^2)); v

a(n) = A020639(A000005(n)).
a(A108951(n)) = A329614(n). - Antti Karttunen, Nov 17 2019
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - Amiram Eldar, Jan 15 2024

Data section extended up to term a(105) by Antti Karttunen, Nov 17 2019

A369209 Numbers whose number of divisors has the largest prime factor 3.

Original entry on oeis.org

4, 9, 12, 18, 20, 25, 28, 32, 36, 44, 45, 49, 50, 52, 60, 63, 68, 72, 75, 76, 84, 90, 92, 96, 98, 99, 100, 108, 116, 117, 121, 124, 126, 132, 140, 147, 148, 150, 153, 156, 160, 164, 169, 171, 172, 175, 180, 188, 196, 198, 200, 204, 207, 212, 220, 224, 225, 228

Offset: 1

Amiram Eldar, Jan 16 2024

Subsequence of A059269 and first differs from it at n = 36: A059269(136) = 44 has 15 = 3 * 5 divisors and thus is not a term of this sequence.
Numbers k such that A000005(k) is in A065119.
Numbers k such that A071188(k) = 3.
Equals the complement of A354181, without the terms of A036537 (i.e., complement(A354181) \ A036537).
The asymptotic density of this sequence is Product_{p prime} (1-1/p) * (Sum_{k>=1} 1/p^(A003586(k)-1)) - A327839 = 0.26087647470200496716... .

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A003586, A006530, A036537, A065119, A336595, A071188, A211337, A211338, A327839, A354181.
Subsequence of A013929 and A059269.
Subsequences: A001248, A030627, A050997, A054753, A062503, A067259, A079395, A085986, A085987, A086975, A095990, A096156, A138032, A162143, A179643, A179645.

gpf[n_] := FactorInteger[n][[-1, 1]]; Select[Range[300], gpf[DivisorSigma[0, #]] == 3 &]

gpf(n) = if(n == 1, 1, vecmax(factor(n)[, 1]));
is(n) = gpf(numdiv(n)) == 3;

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A078545 Duplicate of A071188.

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A071190 Greatest prime factor of sum of divisors of n, for n >= 2; a(1) = 1.

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A071187 Smallest prime factor of number of divisors of n; a(1) = 1.

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A369209 Numbers whose number of divisors has the largest prime factor 3.

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