A327713 Exceptional class of numbers k such that p(25*k + 24) == 0 (mod 125), where p() = A000041().

6, 26, 60, 65, 70, 81, 96, 126, 135, 141, 175, 176, 196, 205, 206, 226, 305, 310, 330, 340, 346, 371, 380, 435, 436, 440, 460, 480, 481, 516, 595, 611, 646, 650, 665, 666, 685, 696, 700, 710, 716, 725, 730, 736, 745, 751, 760, 765, 775, 780, 811, 826, 841, 860, 871

Offset: 1

Author

Petros Hadjicostas, Sep 23 2019

Keywords

• nonn

Comments

The unexceptional class consists of the numbers k == (2, 3, or 4) (mod 5). Watson (1938, p. 111) proved that such numbers k satisfy p(25*k + 24) == 0 (mod 125).

(p(25*a(m) + 24)/125: m >= 1) = (3177000598, 140513239982045202108972, 23104937422373952975695974907848646058, ...).

Examples

			p(25*6 + 24) = p(174) = 397125074750 = 3177000598 * 125 (the only example in Watson (1938)).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Watson, G. N., Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle) 179 (1938), 97-128; see pp. 111-113.

Crossrefs

Cf. A000041, A071734, A110375, A160524, A327714.

Programs

PARI

is(n) = n % 5 < 2 && numbpart(25*n+24)%125==0 \\ David A. Corneth, Sep 23 2019

Extensions

More terms from David A. Corneth, Sep 23 2019