A073932 -id:A073932 - cp's OEIS frontend

A073934 Sum of terms in n-th row of triangle in A073932.

1, 3, 6, 7, 12, 12, 19, 15, 21, 22, 33, 24, 37, 33, 37, 31, 48, 39, 58, 42, 54, 55, 78, 48, 67, 63, 66, 61, 90, 67, 98, 63, 88, 82, 96, 75, 112, 96, 102, 82, 123, 96, 139, 99, 112, 124, 171, 96, 145, 117, 133, 115, 168, 120, 154, 117, 153, 148, 207, 127, 188, 160

Offset: 1

Amarnath Murthy, Aug 19 2002

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A032742, A060681, A073932, A073933, A073935.

a[1] := 1:for i from 2 to 500 do n := i:s := n:while(n>1) do if isprime(n) then r := n-1: else r := n-n/ifactors(n)[2][1][1]; fi; n := r:s := s+n:od:a[i] := s:od:seq(a[k],k=1..500);

Array[If[# == 1, 1, Total@ NestWhileList[If[PrimeQ@ #, # - 1, # - #/FactorInteger[#][[1, 1]] ] &, #, # > 1 &]] &, 62]

(define (A073934 n) (if (= 1 n) n (+ n (A073934 (A060681 n)))))
(define (A060681 n) (- n (A032742 n))) ;; See also code under A032742
;; Antti Karttunen, Aug 23 2017

a(1) = 1; for n > 1, a(n) = n + a(A060681(n)). - Antti Karttunen, Aug 23 2017

More terms from Sascha Kurz, Aug 23 2002

Offset corrected from 0 to 1 by Antti Karttunen, Aug 23 2017

A073933 Number of terms in n-th row of triangle in A073932.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 6, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 7, 7, 8, 7, 8, 6, 8, 7, 8, 7, 8, 8, 8, 7, 8, 8, 9, 8, 8, 9, 10, 7, 9, 8, 8, 8, 9, 8, 9, 8, 9, 9, 10, 8, 9, 9, 9, 7, 9, 9, 10, 8, 10, 9, 10, 8, 9, 9, 9, 9, 10, 9, 10, 8, 9, 9, 10, 9, 9, 10, 10, 9, 10, 9, 10, 10, 10, 11, 10, 8

Offset: 1

Amarnath Murthy, Aug 19 2002

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A032742, A060681, A073932, A073934, A073935.

One more than A064097.

a[1] := 1:for i from 2 to 500 do n := i:s := 1:while(n>1) do if isprime(n) then r := n-1: else r := n-n/ifactors(n)[2][1][1]; fi; n := r:s := s+1:od:a[i] := s:od:seq(a[k],k=1..500);

(define (A073933 n) (if (= 1 n) n (+ 1 (A073933 (A060681 n)))))
(define (A060681 n) (- n (A032742 n))) ;; See also code under A032742
;; Antti Karttunen, Aug 23 2017

From Antti Karttunen, Aug 23 2017: (Start)
a(1) = 1; for n > 1, a(n) = 1 + a(A060681(n)).
a(n) = 1 + A064097(n).
(End)

More terms from Sascha Kurz, Aug 23 2002

Offset corrected from 0 to 1 by Antti Karttunen, Aug 23 2017

A073935 Numbers n such that the n-th row of triangle in A073932 contains exactly the divisors of n.

Original entry on oeis.org

1, 2, 4, 6, 8, 16, 18, 20, 32, 42, 54, 64, 100, 128, 162, 256, 272, 294, 342, 486, 500, 512, 1024, 1458, 1806, 2048, 2058, 2500, 4096, 4374, 4624, 6498, 8192, 10100, 12500, 13122, 14406, 16384, 26406, 32768, 39366, 62500, 65536, 65792, 77658

Offset: 1

Amarnath Murthy, Aug 19 2002

nonn

John Machacek, Egyptian Fractions and Prime Power Divisors, arXiv:1706.01008 [math.NT], 2017.

Cf. A073932, A073933, A073934, A283423.

More terms from Sascha Kurz, Aug 23 2002

Name clarified by Sean A. Irvine, Dec 28 2024

A074093 Number of values of k such that n = k - largest divisor of k (

Original entry on oeis.org

1, 2, 1, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 1, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 3, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 4, 1, 1, 1

Offset: 1

Amarnath Murthy, Aug 19 2002

nonn

			a(6) = 3 and the three values of k are 7,9 and 12.

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A073932, A073933, A073934, A073935, A060681.

f1[n_] := Count[Range[n, 2 n], ?(Differences[Take[Divisors[#], -2]] == {n} &)]; Join[{1}, Table[f1[n], {n, 2, 105}]] (* _Jayanta Basu, Jul 30 2013 *)

a(n)=sum(k=2,2*n,if(k- component(divisors(k),numdiv(k)-1)-n,0,1))

a(2n+1)=1; sum(k=1, n, a(k)) seems to be asymptotic to C*n with C=1.6... - Benoit Cloitre, Aug 21 2002

More terms from Benoit Cloitre and Vladeta Jovovic, Aug 21 2002

cp's OEIS Frontend

A073934 Sum of terms in n-th row of triangle in A073932.

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A073933 Number of terms in n-th row of triangle in A073932.

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A073935 Numbers n such that the n-th row of triangle in A073932 contains exactly the divisors of n.

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A074093 Number of values of k such that n = k - largest divisor of k (

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