A380304 -id:A380304 - cp's OEIS frontend

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

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).

A380303 Numbers m such that GCD of the solutions x to sigma(x) = sigma(m) are setwise coprime.

Original entry on oeis.org

1, 6, 10, 11, 14, 15, 16, 17, 20, 21, 23, 24, 25, 26, 28, 30, 31, 33, 34, 35, 38, 39, 40, 41, 42, 44, 46, 47, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 65, 66, 69, 70, 71, 74, 76, 77, 78, 79, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 99, 102, 103, 105, 107, 108, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 123, 124, 125, 126, 127, 130, 131, 132, 135, 136, 138, 139, 140, 141, 142, 143, 145, 147, 150

Offset: 1

Max Alekseyev, Jan 19 2025

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Cf. A206036, A211656, A241480, A241481, A241625, A380304.

isok(k) = if(k == 1, 1, my(v = invsigma(sigma(k))); #v > 1 && gcd(v) == 1); \\ Amiram Eldar, May 28 2025, using Max Alekseyev's invphi.gp (see links).

Union of {1} and the set difference of A206036 and A241481.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

PARI

Formula

A380303 Numbers m such that GCD of the solutions x to sigma(x) = sigma(m) are setwise coprime.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula