A072808 -id:A072808

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A333633

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

+10
1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

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

LINKS

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

PROG

(PARI) 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

CROSSREFS

Bisection of A072808.

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

KEYWORD

nonn

AUTHOR

Michel Marcus, Mar 30 2020

EXTENSIONS

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

STATUS

approved

A333847

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

+10
1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

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

LINKS

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

PROG

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