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 A064028 #21 Jun 02 2025 13:20:00 %S A064028 1,3,12,36,216,1020,8160,61920,507744,4383392,52600704,624249600, %T A064028 8739494400,109190390400,1583122968000,25318378008000,455730804144000, %U A064028 8193040840252800,163860816805056000,3256371347261760000,67204676251838361600,1366492477414792734720 %N A064028 Sum of the unitary divisors of n!. %H A064028 Amiram Eldar, <a href="/A064028/b064028.txt">Table of n, a(n) for n = 1..450</a> %H A064028 Charles R. Wall, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/22-3/advanced22-3.pdf">Problem H-374</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 22, No. 3 (1984), p. 280; <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/24-2/advanced24-2.pdf">Bounds of Joy</a>, Solution to Problem H-374 by the proposer, ibid., Vol. 24, No. 2 (1986), p. 188. %F A064028 a(n) = usigma(n!) = A034448(A000142(n)). %F A064028 a(n)/n! <= 2 (while usigma(n)/n and sigma(n!)/n! are unbounded; Wall, 1984). - _Amiram Eldar_, Feb 08 2022 %e A064028 n=6, 6! = 720, sum of the 8 unitary ones of its 30 divisors is 1020, a(6) = 720+1+16+45+9+80+5+144 = 1020. %t A064028 usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); usigma/@ (Range[17]!) (* _Amiram Eldar_, Jun 23 2019 *) %o A064028 (PARI) valp(n,p)=my(s); while(n\=p, s+=n); s %o A064028 a(n)=my(s=1); forprime(p=2,n, s*=p^valp(n,p)+1); s \\ _Charles R Greathouse IV_, Jan 26 2023 %Y A064028 Cf. A034448, A046656, A056657, A056171, A056172, A000203, A000142, A062569. %K A064028 nonn %O A064028 1,2 %A A064028 _Labos Elemer_, Sep 11 2001