A074583 - OEIS

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A074583

Numbers k such that sopfr(k) = S(k), where sopfr = A001414 and S = A002034.

1, 2, 3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

These are the prime powers p^e with e <= p. - Reinhard Zumkeller, Dec 15 2003

Complement to A192135 with respect to A000961;

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000961(A192188(n)); A095874(a(n)) = A192188(n). - Reinhard Zumkeller, Jun 26 2011

MATHEMATICA

sopfr[n_] := Total[Times @@@ FactorInteger[n]];

S[n_] := Module[{m = 1}, While[!IntegerQ[m!/n], m++]; m];

Select[Range[1000], sopfr[#] == S[#]&] (* Jean-François Alcover, Nov 09 2017 *)

PROG

(Haskell)

import Data.Set (singleton, deleteFindMin, insert)

a074583 n = a074583_list !! (n-1)

a074583_list = 1 : f (singleton 2) a000040_list where

f s ps'@(p:p':ps)

| m == p = p : f (insert (p*p) $ insert p' s') (p':ps)

| m < spf^spf = m : f (insert (m*spf) s') ps'

| otherwise = m : f s' ps'

where spf = a020639 m -- smallest prime factor of m, cf. A020639

(m, s') = deleteFindMin s

-- Simpler version:

a074583_list = map a000961 a192188_list

-- Reinhard Zumkeller, Jun 05 2011, Jun 26 2011

(PARI) isok(n) = my(f=factor(n)); n==1 || (#f~==1 && f[1, 1]>=f[1, 2]); \\ Seiichi Manyama, May 07 2021

CROSSREFS

Subsequence of A000961; A000040, A000430, and A051674 are subsequences.

Cf. A095874, A192135, A192188, A343983.

Sequence in context: A325266 A284288 A343983 * A001092 A327782 A000430

Adjacent sequences: A074580 A074581 A074582 * A074584 A074585 A074586

KEYWORD

easy,nonn

AUTHOR

Jason Earls, Aug 24 2002

STATUS

approved