A007370 Numbers k such that sigma(x) = k has a unique solution. (Formerly M2319)

1, 3, 4, 6, 7, 8, 13, 14, 15, 20, 28, 30, 36, 38, 39, 40, 44, 57, 62, 63, 68, 74, 78, 91, 93, 102, 110, 112, 121, 127, 133, 138, 150, 158, 160, 162, 164, 171, 174, 176, 183, 194, 195, 198, 200, 204, 212, 217, 222, 230, 242, 255, 256, 258, 260, 266, 278, 282

Offset

1,2

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

Wacław Sierpiński, Elementary Theory of Numbers, Państ. Wydaw. Nauk., Warsaw, 1964, p. 165.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Wacław Sierpiński, Elementary Theory of Numbers, Warszawa, 1964.

Robert G. Wilson v, Letter to N. J. A. Sloane, Jul. 1992.

Mathematica

a = Table[ 0, {250} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 251, a[ [ s ] ]++ ], {n, 1, 250} ]; Select[ Range[ 250 ], a[ [ # ] ] == 1 & ]

Prog

(PARI) list(lim)=my(v=vectorsmall(lim\1), u=List(), s); for(k=1, #v, s=sigma(k); if(s<=#v, v[s]++)); for(k=1, #v, if(v[k]==1, listput(u, k))); Vec(u) \\ Charles R Greathouse IV, Jun 15 2015
(PARI) is(k) = invsigmaNum(k) == 1 \\ Amiram Eldar, Nov 18 2024, using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000203.

Number of solutions: A007369 (0), this sequence (1), A007371 (2), A007372 (3), A060660 (4), A060661 (5), A060662 (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), A060676 (12).

Sequence in context: A108348 A085149 A239458 * A322376 A376424 A044813

Adjacent sequences: A007367 A007368 A007369 * A007371 A007372 A007373

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Status

approved