A072808 -id:A072808 - cp's OEIS frontend

A333633 Smallest m such that sigma(m) == 2*n (mod phi(m)) or 0 if no solution exists.

1, 5, 24, 22, 21, 40, 48, 136, 110, 90, 88, 656, 102, 80, 96, 68, 55, 464, 65, 117, 91, 116, 85, 272, 95, 148, 133, 164, 115, 160, 147, 333, 247, 212, 145, 243968, 155, 244, 217, 405, 230, 11072, 185, 292, 259, 1184, 205, 237824, 215, 657, 301, 356, 189, 343, 329, 388, 559, 404

Offset: 0

Michel Marcus, Mar 30 2020

nonn

a(221) <= 288230257234804736 = 2^(k-2)*(2^k-443) for k=30. - Michel Marcus, Apr 02 2020

a(221) > 10^13. - Giovanni Resta, Apr 12 2020

Michel Marcus, Table of n, a(n) for n = 0..220

Bisection of A072808.

Cf. A000203, A000010, A063514, A067192, A067193.

g(n) = my(f=factor(n)); sigma(f) % eulerphi(f);
a(n) = {n *= 2; my(k=1); while (g(k) != n, k++); k;} \\ Michel Marcus, Mar 30 2020

a(0) prepended by Jinyuan Wang, Mar 30 2020

A333847 a(n) = A063514(A028982(n)).

Original entry on oeis.org

0, 0, 1, 3, 1, 7, 3, 11, 15, 7, 15, 13, 31, 3, 13, 3, 17, 23, 63, 19, 39, 27, 63, 65, 43, 69, 127, 51, 35, 91, 81, 39, 15, 1, 237, 9, 51, 255, 47, 115, 105, 281, 87, 33, 117, 121, 87, 33, 59, 207, 181, 63, 235, 511, 141, 409, 243, 517, 87, 343, 295, 249, 75, 615, 363

Offset: 1

Michel Marcus, Apr 08 2020

nonn

Except for the first 2 terms, all terms are odd.

Michel Marcus, Table of n, a(n) for n = 1..5000

Cf. A028982 (squares and twice squares), A063514 (sigma(n) mod phi(n)), A072808.

lista(nn) = {for (n=1, nn, if (issquare(n) || (!(n%2) && issquare(n/2)), print1(sigma(n) % eulerphi(n), ", ");););}

cp's OEIS Frontend

A333633 Smallest m such that sigma(m) == 2*n (mod phi(m)) or 0 if no solution exists.

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