OFFSET
1,3
COMMENTS
Data extracted from A002961.
The terms were calculated by:
a(1)-a(4) - Andrzej Makowski (1960)
a(5) - Mientka & Vogt (1970), Lal, Eldridge & Gillard (1972)
a(6)-a(7) - Hunsucker, Nebb & Stearns (1973)
a(8) - Pentti Haukkanen (1993)
a(9) - Jud McCranie (1997)
a(10) - T. D. Noe (2007)
a(11)-a(12) - T. D. Noe (2010)
a(13) - Giovanni Resta (2014)
REFERENCES
John L. Hunsucker, Jack Nebb, and Robert E. Stearns, Jr., Computational results concerning some equations involving sigma(n), The Mathematics Student, Vol. 41 (1973), pp. 285-289.
LINKS
Pentti Haukkanen, Some computational results concerning the divisor functions d(n) and sigma(n), The Mathematics Student, Vol. 62 (1993), pp. 166-168.
M. Lal, C. Eldridge & P. Gillard, Solutions of sigma(n) = sigma(n+k), 1972, Review in Mathematics of Computation, Vol. 27, No. 123 (1973), p. 676.
Andrzej Makowski, On Some Equations Involving Functions phi(n) and sigma(n), The American Mathematical Monthly, Vol. 67, No. 7 (1960), pp. 668-670; Correction, ibid., Volume 68, No. 7 (1961), p. 650.
Walter E. Mientka and Richard L. Vogt, Computational results relating to problems concerning sigma(n), Matematicki Vesnik, Vol. 7, No. 51 (1970), pp. 35-36.
FORMULA
Conjecture: Limit_{n->oo} a(n)/A300285(n) = 1.
EXAMPLE
Below 10^3 there are 3 solutions x = 14, 206, 957, hence a(3) = 3.
MATHEMATICA
With[{s = Array[DivisorSigma[1, #]&, 10^5]}, Array[Count[Range[10^# - 1], _?(s[[#]] == s[[# + 1]] &)] &, IntegerLength@ Length@ s - 1]] (* after Michael De Vlieger at A300285 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jul 29 2018
STATUS
approved