A324553 -id:A324553 - cp's OEIS frontend

A009191 a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005).

1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 6, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 9, 1, 2, 1, 8, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 8, 1, 2, 1, 12, 1, 2, 3, 1, 1, 2, 1, 2, 1, 2, 1, 12, 1, 2, 3, 2, 1, 2, 1, 10, 1, 2, 1, 12, 1, 2, 1, 8, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 3, 1, 1, 2, 1, 8, 1

Offset: 1

David W. Wilson

nonn

a(A046642(n)) = 1.
First occurrence of k: 1, 2, 9, 8, 400, 12, 3136, 24, 36, 80, 123904, 60, 692224, 448, 2025, 384, .... Conjecture: each k is present. - Robert G. Wilson v, Mar 27 2013
Conjecture is true. See David A. Corneth's comment in A324553. - Antti Karttunen, Mar 06 2019

Antti Karttunen, Table of n, a(n) for n = 1..65537 (terms 1..1000 from T. D. Noe)

Cf. A000005, A009194, A009195, A009205, A009213, A009230, A049820, A125168, A138010, A286540, A303781, A318459, A319337, A322979, A322980, A323073.

Cf. A046642 (positions of ones), A324553 (position of the first occurrence of each n).

a009191 n = gcd n $ a000005 n
-- Reinhard Zumkeller, May 09 2013, Aug 14 2011

f[n_] := GCD[n, DivisorSigma[0, n]]; Array[f, 105] (* Robert G. Wilson v, Mar 27 2013 *)

a(n)=gcd(numdiv(n),n) \\ Charles R Greathouse IV, Mar 26 2013

a(n) = gcd(n, A000005(n)) = gcd(n, A049820(n)). - Antti Karttunen, Sep 25 2018

A324554 a(n) = the smallest number m such that gcd(tau(m), sigma(m)) = n where tau(k) = the number of the divisors of k (A000005) and sigma(k) = the sum of the divisors of k (A000203).

Original entry on oeis.org

1, 3, 18, 6, 648, 20, 2916, 30, 288, 304, 82944, 60, 36864, 832, 16200, 168, 5509980288, 612, 31719424, 432, 23328, 44032, 247669456896, 420, 9487368, 258048, 14112, 2496, 31581162962944, 4176, 26843545600, 840, 4064256, 4390912, 42693156, 1980, 151801324109824

Offset: 1

Jaroslav Krizek, Mar 05 2019

nonn

a(n) = the smallest number m such that A009205(m) = n.

a(p) = q^(c*p-1) * k for p prime, where q is some prime, c and k are positive integers. - David A. Corneth, Mar 07 2019

			For n=3; a(3) = 18 because gcd(tau(18), sigma(18)) = gcd (6, 39) = 3 and 18 is the smallest.

Cf. A000005, A007955, A009205.

Cf. also A324553, A324555.

[Min([n: n in[1..10^5] | GCD(NumberOfDivisors(n), SumOfDivisors(n)) eq k]): k in [1..16]]

Array[Block[{m = 1}, While[GCD @@ DivisorSigma[{0, 1}, m] != #, m++]; m] &, 16] (* Michael De Vlieger, Mar 24 2019 *)

A324554search_and_print(searchlimit) = { my(m = Map(), k); for(n=1,searchlimit,k=gcd(sigma(n),numdiv(n)); if(!mapisdefined(m,k), mapput(m,k,n))); for(k=1, oo, if(!mapisdefined(m,k), break, print1(mapget(m,k), ", "))); }; \\ Antti Karttunen, Mar 06 2019

a(17)-a(37) from Jon E. Schoenfield, Mar 06 2019

cp's OEIS Frontend

A009191 a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005).

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