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 A304294 Numbers k having at least one divisor d such that sigma(k) = sigma(k+d). 1
 14, 54, 154, 182, 206, 220, 238, 264, 266, 270, 284, 322, 366, 406, 434, 518, 574, 594, 602, 658, 660, 702, 742, 826, 834, 848, 852, 854, 918, 938, 957, 994, 1022, 1026, 1030, 1106, 1162, 1240, 1242, 1246, 1334, 1350, 1358, 1364, 1392, 1414, 1420, 1442, 1498, 1504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first number that admits two different divisors is 702: two of its divisors are 6 and 26, and sigma(702) = sigma(702 + 6) = sigma(702 + 26) = 1680. The first number that admits three different divisors is 11934: three of its divisors are 26, 102, and 442, and sigma(11934) = sigma(11934 + 26) = sigma(11934 + 102) = sigma(11934 + 442) = 30240. LINKS EXAMPLE One divisor of 14 is 1 and sigma(14) = sigma(14 + 1) = 24. One divisor of 54 is 2 and sigma(54) = sigma(54 + 2) = 120. MAPLE with(numtheory): P:=proc(n) local a, k, ok; a:=divisors(n); ok:=0; for k from 1 to nops(a) do if sigma(n)=sigma(n+a[k]) then ok:=1; fi; od; if ok=1 then n; fi; end: seq(P(i), i=1..1504); MATHEMATICA Select[Range[2000], Function[k, AnyTrue[Divisors@ k, DivisorSigma[1, k] == DivisorSigma[1, k + #] &]]] (* Michael De Vlieger, May 14 2018 *) PROG (PARI) isok(n) = sumdiv(n, d, sigma(n+d) == sigma(n)) > 0; \\ Michel Marcus, May 14 2018 CROSSREFS Cf. A000203, A304295. Sequence in context: A048971 A299646 A006597 * A114012 A140784 A022285 Adjacent sequences:  A304291 A304292 A304293 * A304295 A304296 A304297 KEYWORD nonn,easy AUTHOR Paolo P. Lava, May 14 2018 STATUS approved

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Last modified December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)