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A327713 Exceptional class of numbers n such that p(25*n + 24) == 0 mod 125, where p() = A000041(). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

Watson, G. N., Ramanujans Vermutung √ľber Zerf√§llungsanzahlen, J. Reine Angew. Math. (Crelle) 179 (1938), 97-128; see pp. 111-113.

EXAMPLE

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

PROG

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

CROSSREFS

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

Sequence in context: A075456 A166728 A285453 * A136892 A254527 A190095

Adjacent sequences:  A327710 A327711 A327712 * A327714 A327715 A327716

KEYWORD

nonn

AUTHOR

Petros Hadjicostas, Sep 23 2019

EXTENSIONS

More terms from David A. Corneth, Sep 23 2019

STATUS

approved

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Last modified August 8 14:36 EDT 2020. Contains 336298 sequences. (Running on oeis4.)