A380303 -id:A380303 - cp's OEIS frontend

A380304 a(n) = sigma(A380303(n)).

1, 12, 18, 12, 24, 24, 31, 18, 42, 32, 24, 60, 31, 42, 56, 72, 32, 48, 54, 48, 60, 56, 90, 42, 96, 84, 72, 48, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 96, 104, 84, 144, 96, 144, 72, 114, 140, 96, 168, 80, 84, 224, 108, 132, 120, 180, 90, 234, 168, 128, 144, 120, 252, 98, 156, 216, 104, 192, 108, 280, 216, 152, 248, 114, 240, 144, 182, 180, 144, 360, 168, 224, 156, 312, 128, 252, 132, 336, 240, 270, 288, 140, 336, 192

Offset: 1

Max Alekseyev, Jan 19 2025

nonn

Except for a(1)=1, subsequence of A206421.

Cf. A000203, A206036, A211656, A241480, A241481, A241625, A380303.

a(n) = sigma(A380303(n)) = A000203(A380303(n)).

A241625 Smallest number m such that the GCD of the x's that satisfy sigma(x)=m is n.

Original entry on oeis.org

1, 3, 4, 7, 6, 6187272, 8, 15, 13, 196602, 8105688, 28, 14

Offset: 1

Michel Marcus, Apr 26 2014

This sequence is a sequel to A240667.
Some large known terms: a(16)=2031554, a(25)=1355816, a(31)=8880128, a(80)=11532, a(97)=5488.
a(14) > 10^9. - Michel Marcus, May 09 2014
a(n) is a multiple of A353783(n). Some further terms: a(15) = 497943732, a(17) = 962949708, a(20) = 612372264, a(48) = 12692888, a(53) = 39887316. - Max Alekseyev, Jan 19 2025

			a(2) = 3, because the only x such that sigma(x)=3 is 2.
a(6) = 6187272, because the x's that satisfy sigma(x)=6187272 are [2651676, 2855646] and their GCD is 6.

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Cf. A000203, A211656, A240667, A353783, A380303, A380304.

lista() = {lim = 12000000; nn = 100; out = "a241625.txt"; v = vector(lim, i, sigma(i)); w = vector(lim); for (i=1, lim, vi = v[i]; if (vi <= lim, if (w[vi] == 0, w[vi] = i, w[vi] = concat(w[vi], i)););); for (i=1, nn, got = 0; write1(out, i, " "); for (j=1, #w, wj = w[j]; if (gcd(wj) == i, got = 1; write(out, j);break;);); if (! got, write(out, );););}

a(n) = my(m=1); while(gcd(invsigma(m)) != n, m++); m; \\ Michel Marcus, Jan 16 2025; using Max Alekseyev's invphi.gp

For n in A211656, a(n) = sigma(n).

cp's OEIS Frontend

A380304 a(n) = sigma(A380303(n)).

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A241625 Smallest number m such that the GCD of the x's that satisfy sigma(x)=m is n.

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