This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081378 #19 Mar 25 2024 06:45:59
%S A081378 412,1142,1236,1328,1339,1703,2855,2875,2884,3406,3426,3668,3708,3984,
%T A081378 4017,5109,5356,5710,5750,5924,6003,6281,6399,6413,6640,6812,7994,
%U A081378 8054,8318,8515,8565,8611,8625,8652,8843,8858,9373,9707,9991
%N A081378 Numbers k for which the sums of prime factors (ignoring multiplicity) of sigma(k) and phi(k) are equal but the sets of prime factors of sigma and phi are different.
%H A081378 Amiram Eldar, <a href="/A081378/b081378.txt">Table of n, a(n) for n = 1..10000</a>
%e A081378 k = 412 = 2*2*103: sigma(412) = 728 = 2*2*2*7*13, phi(412) = 204 = 2*2*3*17, the sums of prime factors are identical (2 + 7 + 13 = 22 = 2 + 3 + 17) but the prime sets are different: {2,7,13} vs. {2,7,17}.
%t A081378 ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; spf[x_] := Apply[Plus, ba[x]]; k=0; Do[s=ba[DivisorSigma[1, n]]; s1=ba[EulerPhi[n]]; s3=spf[DivisorSigma[1, n]]; s4=spf[EulerPhi[n]]; If[ !Equal[s, s1]&&Equal[s3, s4], k=k+1; Print[{n, s, s1, ba[n], s3}]], {n, 1, 10000}]
%o A081378 (PARI) is(n) = {my(f = factor(n), p1 = factor(sigma(f))[, 1], p2 = factor(eulerphi(f))[, 1]); p1 != p2 && vecsum(p1) == vecsum(p2) ;} \\ _Amiram Eldar_, Mar 25 2024
%Y A081378 Cf. A000010, A000203, A065642, A076533, A081377.
%K A081378 nonn
%O A081378 1,1
%A A081378 _Labos Elemer_, Mar 26 2003