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A371420
Greater member of Carmichael's variant of amicable pair: numbers k < m such that s(k) = m and s(m) = k, where s(k) = A371418(k).
2
14, 62, 124, 189, 254, 508, 2032, 16382, 32764, 131056, 262142, 524284, 524224, 1048574, 2097148, 2097136, 8388592, 8388544, 33554368, 536866816, 2147479552, 4294967294, 8589934588, 34359738352, 34359672832, 137438953408
OFFSET
1,1
COMMENTS
The terms are ordered according to their lesser counterparts (A371419).
LINKS
Robert D. Carmichael, Empirical Results in the Theory of Numbers, The Mathematics Teacher, Vol. 14, No. 6 (1921), pp. 305-310; alternative link. See p. 309.
EXAMPLE
14 is a term since A371418(14) = 12 < 14, and A371418(12) = 14.
MATHEMATICA
r[n_] := n/FactorInteger[n][[1, 1]]; s[n_] := r[DivisorSigma[1, n]]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 1, 10^6}]; seq
PROG
(PARI) f(n) = {my(s = sigma(n)); if(s == 1, 1, s/factor(s)[1, 1]); }
lista(nmax) = {my(m); for(n = 1, nmax, m = f(n); if(m > n && f(m) == n, print1(m, ", "))); }
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Mar 23 2024
STATUS
approved